C₂×#23761356 #34197969

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×#23761356

Splittings

Fitting	C₂×C₄×C₁₆×C₇₉ ⋊ C₂
Sylow	C₇₉ ⋊ C₂×D₄⋊C₁₆

Subgroups

	subgroup	G/H
center	C₂²×C₈	D₃₁₆
commutator	C₄×C₇₉	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₇₉
Fitting	C₂×C₄×C₁₆×C₇₉	C₂
socle	C₂³×C₇₉	C₂²⋊C₈
prime radical	C₂²×D₃₁₆	C₈
cosocle	C₄×C₈×C₇₉	C₂³
hypercenter	C₂×C₄×C₁₆	D₇₉
hypocenter	C₇₉	C₂×D₄⋊C₁₆
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 10112

A minimal faithful permutation representation — 3 generators on 105 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)(83,86)(84,89)(87,88);(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)(82,83)(84,86)(85,88)(87,89)(90,91,92,95,93,96,98,101,94,97,99,102,100,103,104,105);(80,81)

Conjugacy classes & character table

5104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 79268);

C2×#23761356 #34197969