#27079702

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

No aliases for this group.

Splittings

Sylow

C₄₇ ⋊ #60058

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Fitting	C₂×C₄₇×#568	C₂
socle	C₂²×C₄₇	C₂⁴×C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#568	D₄₇
hypocenter	C₄₇	#60058
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#568

3178 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)(54,63)(58,69)(62,74)(64,76)(68,78)(70,80)(75,82)(79,83);(55,65)(59,71)(62,74)(66,77)(68,78)(72,81)(75,82)(79,83);(52,55)(53,59)(54,62)(56,66)(57,65)(58,68)(60,72)(61,71)(63,74)(64,75)(67,77)(69,78)(70,79)(73,81)(76,82)(80,83);(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)(52,54)(53,58)(55,62)(56,64)(57,63)(59,68)(60,70)(61,69)(65,74)(66,75)(67,76)(71,78)(72,79)(73,80)(77,82)(81,83);(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)(52,53,56,60,57,61,67,73)(54,58,64,70,63,69,76,80)(55,59,66,72,65,71,77,81)(62,68,75,79,74,78,82,83)

Polycyclic presentation:

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

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1032992);