D₃×C₇×B(4,𝔽₂) #72244278

order	2688
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁷

Aliases

2036 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 168

A minimal faithful permutation representation — 4 generators on 18 points:

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

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

maximal subgroup of	D₃×D₇×B(4,𝔽₂), D₃×ΓL(1,𝔽₈)×B(4,𝔽₂)
maximal normal subgroup of	D₃×D₇×B(4,𝔽₂), D₃×ΓL(1,𝔽₈)×B(4,𝔽₂)

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

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