#327×C₇₁ #17985458

order	4544
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#327×C₇₁

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄×C₇₁
Frattini, cosocle	C₂²×C₄	C₂²×C₇₁
prime radical	#121×C₇₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ G

90 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:

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

Conjugacy classes & character table

1349 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×#327×C₇₁, C₇₁×#1500, C₇₁×#1501, …
maximal normal subgroup of	C₂×#327×C₇₁, C₇₁×#1500, C₇₁×#1501, …
maximal quotient of	C₇₁×#1270, C₇₁×#1271, C₇₁×#1294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 8);

#327×C71 #17985458