C₇₁×#13717 #31834589

order	18176
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₁×#13717

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₁	#2233
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₁
prime radical	C₇₁×#2218	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₁ ◁ C₂×C₄×C₇₁ ◁ C₂²×C₈×C₇₁ ◁ C₂×M₃₂×C₇₁ ◁ G

170 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 66 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:

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

Conjugacy classes & character table

2201 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 6705);