C₁₁²×C₃⋊D₃ #14546115

order	2178
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁² · Schur multiplier (H₂) = C₃×C₁₁

Aliases

direct product	C₁₁²×C₃⋊D₃
unambiguous semidirect product	C₃⋊(D₃×C₁₁²)

Fitting, socle, Hall	C₃²×C₁₁² ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₁₁²

	subgroup	G/H
center, hypercenter	C₁₁²	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₁²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁²	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₁²

168 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1089

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5,6,7,8,9,10,11)(24,25)(27,28);(12,13,14,15,16,17,18,19,20,21,22)(26,27,28);(23,24,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2178, 32);