C₇₁×#12114 #31832986

order	18176
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₁×#12114

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₇₁
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂×C₄×C₇₁ ◁ C₂×M₁₆×C₇₁ ◁ G

474 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 87
transitive degree	μ_t(G) = 1136

A minimal faithful permutation representation — 3 generators on 87 points:

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

Conjugacy classes & character table

1775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 5102);