D₄₇×#3271 #27091331

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

D₄₇×#3271

Splittings

Fitting	C₄₇×#3271 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3271

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3271	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3271	D₄₇
hypocenter	C₄₇	C₂×#3271
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3271

2826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 67 points:

(5,8,10,16)(6,12,13,20)(7,14,9,18)(11,19,17,15)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(2,4)(5,7,10,9)(6,11,13,17)(8,14,16,18)(12,19,20,15);(5,6,10,13)(7,11,9,17)(8,15,16,19)(12,18,20,14);(1,2)(3,4)(6,11)(7,9)(12,19)(13,17)(14,18)(15,20);(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)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1044621);

D47×#3271 #27091331