C₂×D₃₃₉₂ #27305135

order	13568
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂×D₃₃₉₂

Splittings

Fitting	C₂×C₅₃×C₆₄ ⋊ C₂
Sylow	C₅₃ ⋊ C₂×D₆₄

Subgroups

	subgroup	G/H
center	C₂²	D₁₆₉₆
commutator, cosocle	C₃₂×C₅₃	C₂³
Frattini	C₃₂	C₂²×D₅₃
Fitting	C₂×C₅₃×C₆₄	C₂
socle	C₂²×C₅₃	D₃₂
hypercenter	C₂×C₆₄	D₅₃
hypocenter	C₅₃	C₂×D₆₄
LCS	G ▷ C₃₂×C₅₃ ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 6784

A minimal faithful permutation representation — 3 generators on 119 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)(57,63)(58,69)(59,70)(60,75)(61,79)(64,65)(66,91)(67,93)(68,85)(71,101)(72,104)(73,97)(74,82)(76,110)(77,100)(78,83)(80,108)(81,84)(86,106)(87,105)(88,90)(89,112)(92,116)(94,95)(96,102)(98,99)(103,119)(107,114)(109,113)(111,115)(117,118);(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)(56,57)(58,63)(59,74)(60,78)(61,81)(62,68)(64,69)(65,70)(66,75)(67,79)(71,91)(72,93)(73,85)(76,109)(77,107)(80,111)(82,95)(83,94)(84,102)(86,101)(87,104)(88,97)(89,110)(90,100)(92,108)(96,112)(98,106)(99,105)(103,116)(113,119)(114,118)(115,117);(54,55)

Conjugacy classes & character table

3398 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90611);

C2×D3392 #27305135