#27079960

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

Aliases

No aliases for this group.

Splittings

Fitting	C₄₇×#2911 ⋊ C₂
Sylow	C₄₇ ⋊ #60109

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2911	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2911	D₄₇
hypocenter	C₄₇	#60109
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #2911

2694 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:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(53,59)(57,64)(58,65)(63,67);(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)(54,60)(58,65)(61,66)(63,67);(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)(53,58)(55,61)(56,60)(57,63)(59,65)(62,66)(64,67);(52,53,55,57,56,59,62,64)(54,58,61,63,60,65,66,67);(48,49,50,51)(53,57)(55,62)(58,63)(59,64)(61,66)(65,67)

Polycyclic presentation:

2^8,47|a^2=g,b^2=f,f^2=h,b^a=bf,f^a=fh,e^b=eh,d^c=dh,i^c=i^46,i^d=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, 1033250);