#360×C₇₁ #17985491

order	4544
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

#360×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	#102
commutator	C₈	C₂×C₄×C₇₁
Frattini, cosocle	C₂×C₈	C₂²×C₇₁
prime radical	#135×C₇₁	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂×C₄×C₇₁ ◁ C₂×C₈×C₇₁ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 1136

A minimal faithful permutation representation — 2 generators on 87 points:

(2,6,7,15)(3,9)(4,12)(8,10,13,16)(11,14)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(1,2)(3,10)(4,13)(5,7)(6,14)(8,12)(9,15)(11,16)

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#360×C₇₁, C₇₁×#2145, C₇₁×#2180, …
maximal normal subgroup of	C₂×#360×C₇₁, C₇₁×#2145, C₇₁×#2180, …
maximal quotient of	C₇₁×#1333, C₇₁×#1334, C₇₁×#1347, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 41);

#360×C71 #17985491