D₄₇×#3069 #27083686

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

Aliases

direct product

D₄₇×#3069

Splittings

Fitting	C₄₇×#3069 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3069

Subgroups

	subgroup	G/H
center	C₂	C₂×#121×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3069	C₂
socle	C₂×C₄₇	C₂²×#121
prime radical	#575×D₄₇	C₂
hypercenter	#3069	D₄₇
hypocenter	C₄₇	C₂×#3069
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3069

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 79
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 5 generators on 79 points:

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

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, 1036976);

D47×#3069 #27083686