C₂×#26024375 #36722000

order	22784
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

direct product

C₂×#26024375

Splittings

Fitting	C₂×#379×C₈₉ ⋊ C₂
Sylow	C₈₉ ⋊ C₂×#2472

Subgroups

	subgroup	G/H
center	C₂⁴	C₂³×D₈₉
commutator, cosocle	C₂³×C₈₉	C₂⁵
Frattini	C₂³	C₂⁴×D₈₉
Fitting	C₂×#379×C₈₉	C₂
socle	C₂⁴×C₈₉	C₂⁴
prime radical	C₂²×#15667981	C₂
hypercenter	C₂×#379	D₈₉
hypocenter	C₈₉	C₂×#2472
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×#379

4946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 107
transitive degree	μ_t(G) = 5696

A minimal faithful permutation representation — 5 generators on 107 points:

(7,9,10,8)(12,15)(16,18)(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);(4,6)(7,8,10,9)(11,13,14,17)(12,16,15,18);(3,4)(5,6)(7,8,10,9)(12,15)(16,18)(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);(8,9)(11,12)(13,16)(14,15)(17,18);(1,2)

Conjugacy classes & character table

2540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 337140);

C2×#26024375 #36722000