C₇₁×#9977 #31830849

order	18176
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₁×#9977

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₁	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₇₁
prime radical	C₇₁×#3186	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₁ ◁ C₂³×C₄×C₇₁ ◁ G

544 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 4544

A minimal faithful permutation representation — 3 generators on 103 points:

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

Conjugacy classes & character table

2414 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 2965);