C₇₁×#7402 #31828274

order	18176
nilpotency class	5
isoclinism	isoclinic class of #7402
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₁×#7402

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	#353
commutator	C₂×C₄²	C₂×C₄×C₇₁
Frattini, cosocle	#390	C₂²×C₇₁
prime radical	C₇₁×#2011	C₂
LCS	G ▷ C₂×C₄² ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂³×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ #390×C₇₁ ◁ G

334 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 95
transitive degree	μ_t(G) = 2272

A minimal faithful permutation representation — 2 generators on 95 points:

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

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 390);