D₄₇×#2888 #27079769

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

D₄₇×#2888

Splittings

Fitting	C₄₇×#2888 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2888

Subgroups

	subgroup	G/H
center	C₂	C₂²×C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2888	C₂
socle	C₂×C₄₇	C₂³×C₂²⋊C₄
prime radical	C₂×H(5,𝔽₂)×D₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2888	D₄₇
hypocenter	C₄₇	C₂×#2888
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #2888

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 752

A minimal faithful permutation representation — 5 generators on 63 points:

(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)(50,56)(54,59)(57,62)(61,63);(48,50)(49,54)(51,57)(52,56)(53,59)(55,61)(58,62)(60,63);(49,53)(51,58)(54,59)(57,62);(48,49,51,55,52,53,58,60)(50,54,57,61,56,59,62,63);(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)

Conjugacy classes & character table

1025 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033059);

D47×#2888 #27079769