C₃²×C₇×#120 #72246736

order	2016
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃²×C₇ · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

C₃²×C₇×#120

	subgroup	G/H
center, socle	C₂²×C₃²×C₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₃²×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃²×C₇ ◁ G

780 conjugacy classes of subgroups; only the 312 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 312 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 504

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(3,5)(4,6)(7,8)(9,10,11)(15,16,17,18,19,20,21);(2,5)(6,8)(12,13,14);(2,6)(5,8)

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

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2)(3,5)(4,6)(7,8)(9,10,11)(15,16,17,18,19,20,21), (2,5)(6,8)(12,13,14), (2,6)(5,8));