C₇₁×#23899 #31844771

order	18176
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₇₁×#23899

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ G

1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 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 — 4 generators on 103 points:

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

Conjugacy classes & character table

2840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 16887);