C₂³×C₇×AGL(1,𝔽₇) #72245774

order	2352
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃×C₇ · Schur multiplier (H₂) = C₂⁶

Aliases

	subgroup	G/H
center, hypercenter	C₂³×C₇	AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇	C₂⁴×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂³×C₇²	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂³×C₇

552 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 4 generators on 20 points:

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

392 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((5,6)(7,8,13)(9,10,12)(14,15,16,17,18,19,20), (3,4), (1,2), (8,9)(10,12)(11,13));