C₇₁×#7286 #31828158

order	18176
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₇₁×#7286

Subgroups

	subgroup	G/H
center	C₂×C₄×C₇₁	#99
commutator	C₂²×C₄	C₄²×C₇₁
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₇₁
socle	C₂²×C₇₁	#342
prime radical	C₂³×C₇₁	#95
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₁ ◁ C₂²×C₄×C₇₁ ◁ C₂×C₄×Q₈×C₇₁ ◁ G

250 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 9088

A minimal faithful permutation representation — 2 generators on 103 points:

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

Conjugacy classes & character table

3266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 274);