D₄₇×#2949 #27080408

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

D₄₇×#2949

Splittings

Fitting	C₄₇×#2949 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2949

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2949	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂²×D₄×D₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2949	D₄₇
hypocenter	C₄₇	C₂×#2949
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #2949

2870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 1504

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

(5,7)(6,11)(8,14)(9,13)(10,17)(12,19)(15,20)(16,18)(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);(1,3,4,2)(7,13)(11,19)(14,20)(17,18);(5,6,9,12)(7,11,13,19)(8,16,15,10)(14,18,20,17);(1,2,4,3)(6,10)(7,13)(8,15)(11,18)(12,16)(17,19);(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

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033698);

D47×#2949 #27080408