C₂²×D₈×C₁₉ #11926245

order	1216
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₈×C₁₉

	subgroup	G/H
center, socle	C₂³×C₁₉	D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₁₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

338 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 31 points:

(1,2)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4);(5,6,7,8,9,10,11,12);(6,12)(7,11)(8,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1216, 250);