C₇₁×#10079 #31830951

order	18176
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₁×#10079

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₁	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₁
prime radical	C₂×#496×C₇₁	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂×C₄²×C₇₁ ◁ G

658 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 9088

A minimal faithful permutation representation — 3 generators on 91 points:

(6,11)(7,12)(8,9)(14,17)(15,19)(18,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2)(3,4)(5,6)(7,10)(8,12)(9,11)(15,19)(17,20);(2,4)(5,7,10,6)(8,12,9,11)(13,14)(15,20)(16,18)(17,19)

Conjugacy classes & character table

2414 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 3067);