C₇₁×#12119 #31832991

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

Aliases

direct product

C₇₁×#12119

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

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

normal subgroups only

This group has 404 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)(3,14)(4,8)(5,12)(6,11)(7,13)(9,16)(10,18)(15,27)(17,28)(19,24)(20,26)(21,23)(22,31)(25,32)(29,30)(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);(2,8)(4,18)(5,6)(9,22)(10,12)(11,23)(13,24)(14,27)(15,30)(16,20)(19,21)(25,28)(26,29)(31,32);(1,3,7,17)(2,9,13,26)(4,15,19,32)(5,20,6,16)(8,22,24,29)(10,27,23,25)(11,28,12,14)(18,30,21,31)

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, 5107);