C₂×C₁₉×C₄⋊Q₈ #11926207

order	1216
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×C₁₉×C₄⋊Q₈

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

290 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(4,6)(7,8,11,14)(9,13,10,12);(7,9,11,10)(8,12,14,13);(3,4,5,6)(7,10,11,9)(8,13,14,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1216, 212);