C₂×Dic₂₅₁₂ #34102441

order	20096
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂×Dic₂₅₁₂

Splittings

Sylow

C₁₅₇ ⋊ C₂×Q₆₄

Subgroups

	subgroup	G/H
center	C₂²	D₂₅₁₂
commutator, cosocle	C₁₆×C₁₅₇	C₂³
Frattini	C₁₆	C₂²×D₁₅₇
Fitting	C₂×C₃₂×C₁₅₇	C₂
socle, prime radical	C₂²×C₁₅₇	D₁₆
hypercenter	C₂×C₃₂	D₁₅₇
hypocenter	C₁₅₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₅₇ ▷ C₈×C₁₅₇ ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 223
transitive degree	μ_t(G) = 20096

A minimal faithful permutation representation — 3 generators on 223 points:

(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(160,162,166,176)(161,167,171,192)(163,178,182,212)(164,184,186,218)(165,188,185,175)(168,194,196,221)(169,198,199,223)(170,200,187,191)(172,201,203,177)(173,193,189,180)(174,197,206,179)(181,216,214,211)(183,190,217,219)(195,222,208,205)(202,209,207,215)(204,213,210,220);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(160,161,166,171)(162,172,176,203)(163,177,182,201)(164,183,186,217)(165,187,185,170)(167,189,192,173)(168,193,196,180)(169,197,199,179)(174,205,206,222)(175,207,188,202)(178,198,212,223)(181,215,214,209)(184,194,218,221)(190,216,219,211)(191,204,200,210)(195,213,208,220);(158,159)

Conjugacy classes & character table

5030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20096, 6815);

C2×Dic2512 #34102441