C₂×#125×C₇₁ #17985658

order	4544
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×#125×C₇₁

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₇₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ G

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 89
transitive degree	μ_t(G) = 4544

A minimal faithful permutation representation — 4 generators on 89 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(5,9)(7,10)(11,12,14,16)(13,15,17,18);(3,4,6,8)(5,7,9,10)(11,12)(13,15)(14,16)(17,18);(3,5)(4,7)(6,9)(8,10)(11,13,14,17)(12,15,16,18)

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇₁×#1470, C₂×#330×C₇₁, C₇₁×#1528, …
maximal normal subgroup of	C₇₁×#1470, C₂×#330×C₇₁, C₇₁×#1528, …
maximal quotient of	C₂×#382×C₇₁, C₂×#387×C₇₁, C₂×#389×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 208);

C2×#125×C71 #17985658