C₃²×C₇×#127 #72246346

order	2016
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃²×C₇ · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₃²×C₇×#127

	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

648 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1008

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

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

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