C₂⁴×C₃²×D₇ #72246711

order	2016
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃² · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂⁴×C₃²×D₇

	subgroup	G/H
center, hypercenter	C₂⁴×C₃²	D₇
commutator, cosocle, hypocenter	C₇	C₂⁵×C₃²
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃²×C₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂⁴×C₃²

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

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

maximal subgroup of	C₂⁴×D₇×C₃⋊D₃, C₃²×D₇×#120, D₇×#64162, …
maximal normal subgroup of	C₂⁴×D₇×C₃⋊D₃, C₃²×D₇×#120, D₇×#64162, …

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

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