C₂×#552×D₄₇ #27123262

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₂×#552×D₄₇

Splittings

Fitting	C₂×C₄₇×#552 ⋊ C₂
Sylow	C₄₇ ⋊ C₂²×#552

Subgroups

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#552	C₂
socle	C₂³×C₄₇	C₂⁵
prime radical	C₂²×D₄×D₄₇	C₂²
hypercenter	C₂×#552	D₄₇
hypocenter	C₄₇	C₂²×#552
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#552

7934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 6 generators on 65 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)(60,65)(63,64);(51,55)(54,57)(58,61,62,59)(60,64,65,63);(50,52,53,56)(51,54,55,57)(58,60)(59,63)(61,64)(62,65);(50,51)(52,54)(53,55)(56,57)(58,59,62,61)(60,64,65,63);(48,49)

Conjugacy classes & character table

1250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076552);

C2×#552×D47 #27123262