D₄₇×#2901 #27079873

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

Aliases

direct product

D₄₇×#2901

Splittings

Fitting	C₄₇×#2901 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2901

Subgroups

	subgroup	G/H
center	C₄	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2901	C₂
socle	C₂×C₄₇	C₂³×C₂²⋊C₄
prime radical	#585×D₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2901	D₄₇
hypocenter	C₄₇	C₂×#2901
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #2901

4946 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:

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

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, 1033163);

D47×#2901 #27079873