#27079860

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

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#2898 ⋊ C₂
Sylow	C₄₇ ⋊ #60089

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2898	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×#15689960	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2898	D₄₇
hypocenter	C₄₇	#60089
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ #2898

4902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 3008

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

(1,2)(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)(52,55,57,56)(53,58,60,64)(54,62,61,63)(59,65,66,67);(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)(54,61)(59,66)(62,63)(65,67);(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)(52,54)(53,59)(55,62)(56,63)(57,61)(58,65)(60,66)(64,67);(52,53)(54,59)(55,58)(56,64)(57,60)(61,66)(62,65)(63,67);(48,49,50,51)(53,58)(55,56)(59,65)(60,64)(62,63)(66,67)

Polycyclic presentation:

2^8,47|a^2=g,e^2=h,f^2=h,b^a=bf,e^a=eh,f^a=fh,f^b=fh,d^c=dh,i^c=i^46,i^d=i^46,i^e=i^46

Conjugacy classes & character table

1094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033150);