#27122897

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

No aliases for this group.

Splittings

Sylow

C₄₇ ⋊ #62652

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator	C₂×C₄₇	C₂⁵×C₄
Fitting, prime radical	C₂²×H(5,𝔽₂)×C₄₇	C₂
socle, cosocle	C₂²×C₄₇	C₂⁶
hypercenter	C₂²×H(5,𝔽₂)	D₄₇
hypocenter	C₄₇	#62652
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×H(5,𝔽₂)

11674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 6 generators on 67 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)(53,59)(57,60)(58,65)(64,66);(54,62)(57,60)(61,67)(64,66);(55,63)(58,65)(61,67)(64,66);(52,55)(53,58)(54,61)(56,63)(57,64)(59,65)(60,66)(62,67);(52,54)(53,57)(55,61)(56,62)(58,64)(59,60)(63,67)(65,66);(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)(48,49,50,51)(52,53)(54,60)(55,58)(56,59)(57,62)(61,66)(63,65)(64,67)

Polycyclic presentation:

2^8,47|a^2=h,b^a=bg,f^a=fg,i^a=i^46,e^b=eg,d^c=dg

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076187);