C₂⁴×C₇×C₃⋊D₃ #72246712

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₇ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂⁴×C₇×C₃⋊D₃

	subgroup	G/H
center, hypercenter	C₂⁴×C₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂⁵×C₇
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃²×C₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂⁴×C₇

4488 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 21 points:

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

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

maximal subgroup of	C₂⁴×D₇×C₃⋊D₃, C₇×C₃⋊D₃×#120, C₃⋊D₃×#6516, …
maximal normal subgroup of	C₂⁴×D₇×C₃⋊D₃, C₇×C₃⋊D₃×#120, C₃⋊D₃×#6516, …

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

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