C₂×D₄×C₁₁² #14515562

order	1936
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁² · Schur multiplier (H₂) = C₂³×C₁₁

Aliases

direct product	C₂×D₄×C₁₁²
unambiguous semidirect product	C₄⋊(C₂²×C₁₁²)
unambiguous semidirect product	C₂²⋊(C₂²×C₁₁²)
unambiguous semidirect product	C₂³⋊(C₂×C₁₁²)

	subgroup	G/H
center, socle	C₂²×C₁₁²	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₁₁²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁² ◁ G

378 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 968

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

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

1210 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂×D₄×#10597243, C₂×D₄×C₁₁⋊D₁₁, C₁₁×#66985, …
maximal normal subgroup of	C₂×D₄×#10597243, C₂×D₄×C₁₁⋊D₁₁, C₁₁×#66985, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1936, 156);