C₇₁×#12115 #31832987

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

Aliases

direct product

C₇₁×#12115

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₇₁
prime radical	C₇₁×#2010	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂×C₄×C₇₁ ◁ C₂×M₁₆×C₇₁ ◁ G

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

normal subgroups only

This group has 422 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) = 103
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 3 generators on 103 points:

(1,2)(3,11)(4,15)(5,20)(6,10)(7,12)(8,19)(9,18)(13,31)(14,28)(16,26)(17,27)(21,24)(22,30)(23,32)(25,29)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(1,3,6,14)(2,7,10,22)(4,16,17,32)(5,21,18,13)(8,24,25,31)(9,26,20,23)(11,27,28,15)(12,29,30,19);(4,17)(12,30)(16,32)(19,29)

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, 5103);