C₇₁×#11383 #31832255

order	18176
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₇₁×#11383

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₁	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₇₁
Frattini, cosocle	C₂³×C₄	C₂³×C₇₁
prime radical	C₂⁴×C₇₁	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₁ ◁ C₂²×C₄²×C₇₁ ◁ G

926 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 270 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) = 99
transitive degree	μ_t(G) = 9088

A minimal faithful permutation representation — 3 generators on 99 points:

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

Conjugacy classes & character table

3692 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 4371);