C₂×#23764526 #34315501

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×#23764526

Splittings

Fitting	C₂×#379×C₇₉ ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#2021

Subgroups

	subgroup	G/H
center	C₂³	#14579129
commutator, cosocle	C₂⁴×C₇₉	C₂⁴
Frattini	C₂⁴	C₂³×D₇₉
Fitting	C₂×#379×C₇₉	C₂
socle	C₂³×C₇₉	#120
hypercenter	C₂×#379	D₇₉
hypocenter	C₇₉	C₂×#2021
LCS	G ▷ C₂⁴×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂⁵ ◁ C₂×#379

3986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 93
transitive degree	μ_t(G) = 2528

A minimal faithful permutation representation — 4 generators on 93 points:

(4,6)(7,9)(8,11)(10,13)(12,14)(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);(11,14);(3,4)(5,6)(7,8)(9,11)(10,12)(13,14)(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);(1,2)

Conjugacy classes & character table

2236 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 196800);

C2×#23764526 #34315501