C₃×C₃⋊D₃×#3861 #72230400

order	7938
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

	subgroup	G/H
center, hypercenter	C₃	C₃⋊D₃×#3861
commutator, cosocle, hypocenter	C₃²×C₇²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃³×C₇²	C₂×C₃
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₃

1600 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 882

A minimal faithful permutation representation — 3 generators on 23 points:

(8,9,10,12,11,13,14)(15,16,17)(19,20)(22,23);(2,3,4)(5,7,6)(9,10,11)(12,14,13)(21,22,23);(1,2,3,5,4,6,7)(18,19,20)

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

maximal subgroup of	C₃×C₃⋊D₃×#64424, D₃×C₃⋊D₃×#3861, C₃⋊D₃×C₃⋊#64424, …
maximal normal subgroup of	C₃×C₃⋊D₃×#64424, D₃×C₃⋊D₃×#3861, C₃⋊D₃×C₃⋊#64424, …

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

gap> G := Group((8,9,10,12,11,13,14)(15,16,17)(19,20)(22,23), (2,3,4)(5,7,6)(9,10,11)(12,14,13)(21,22,23), (1,2,3,5,4,6,7)(18,19,20));