C₂×#24907916 #35406185

order	21248
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×#24907916

Splittings

Fitting	C₂³×C₂²⋊C₄×C₈₃ ⋊ C₂
Sylow	C₈₃ ⋊ C₂×#1898

Subgroups

	subgroup	G/H
center	C₂³	C₂×(C₂×D₈₃)⋊C₄
commutator	C₂³×C₈₃	C₂³×C₄
Frattini	C₂⁴	C₂³×D₈₃
Fitting	C₂³×C₂²⋊C₄×C₈₃	C₂
socle	C₂³×C₈₃	C₂×C₂²⋊C₄
prime radical	C₂²×#14581761	C₂
cosocle	C₂⁴×C₈₃	C₂⁴
hypercenter	C₂³×C₂²⋊C₄	D₈₃
hypocenter	C₈₃	C₂×#1898
LCS	G ▷ C₂³×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ C₂³×C₂²⋊C₄

3746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 2656

A minimal faithful permutation representation — 4 generators on 97 points:

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

Conjugacy classes & character table

3344 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 171349);

C2×#24907916 #35406185