C₂×#418×D₄₇ #27079798

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

direct product

C₂×#418×D₄₇

Splittings

Fitting	C₂×C₄₇×#418 ⋊ C₂
Sylow	C₄₇ ⋊ C₂²×#418

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#418	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄×D₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#418	D₄₇
hypocenter	C₄₇	C₂²×#418
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#418

7214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 5 generators on 61 points:

(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);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,58,57)(55,60,61,59);(55,59)(56,57)(60,61);(50,51,52,53)(54,55)(56,60)(57,59)(58,61);(48,49)

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033088);

C2×#418×D47 #27079798