C₂×#24915458 #35610520

order	21248
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁶×C₄²

Aliases

direct product

C₂×#24915458

Splittings

Fitting	C₂²×#120×C₈₃ ⋊ C₂
Sylow	C₈₃ ⋊ C₂×#2812

Subgroups

	subgroup	G/H
center	C₂⁴	C₂³×D₈₃
commutator, cosocle	C₂³×C₈₃	C₂⁵
Frattini	C₂³	C₂⁴×D₈₃
Fitting	C₂²×#120×C₈₃	C₂
socle	C₂⁴×C₈₃	C₂⁴
hypercenter	C₂²×#120	D₈₃
hypocenter	C₈₃	C₂×#2812
LCS	G ▷ C₂³×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#120

4438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 5312

A minimal faithful permutation representation — 5 generators on 105 points:

(9,13)(11,14)(17,22)(20,21)(23,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25);(4,6)(8,12)(11,14)(15,17)(16,20)(18,22)(19,21)(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);(3,4)(5,6)(7,9)(8,11)(10,13)(12,14)(16,19)(17,22);(7,8)(9,11)(10,12)(13,14)(15,16)(17,21)(18,19)(20,22);(1,2)

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 375684);

C2×#24915458 #35610520