#27079844

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

Aliases

No aliases for this group.

Splittings

Fitting	C₂²×#131×C₄₇ ⋊ C₂
Sylow	C₄₇ ⋊ #60086

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×#15689959	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	#60086
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41 ◁ C₂²×#131

4874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 83 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)(52,56,58,57)(53,61,62,70)(54,65,66,71)(55,68,67,69)(59,73,74,63)(60,76,75,80)(64,79,78,81)(72,83,82,77);(55,67)(60,75)(64,78)(68,69)(72,82)(76,80)(77,83)(79,81);(52,55)(53,60)(54,64)(56,68)(57,69)(58,67)(59,72)(61,76)(62,75)(63,77)(65,79)(66,78)(70,80)(71,81)(73,83)(74,82);(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)(55,64)(56,65)(57,71)(58,66)(60,72)(61,73)(62,74)(63,70)(67,78)(68,79)(69,81)(75,82)(76,83)(77,80);(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)(54,63)(55,60)(56,61)(57,70)(58,62)(59,65)(64,77)(66,73)(67,75)(68,76)(69,80)(71,74)(72,79)(78,83)(81,82)

Polycyclic presentation:

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

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033134);