Q₈×D₈×C₁₇ #14526384

order	2176
nilpotency class	3
isoclinism	isoclinic class of D₄×D₈
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

Q₈×D₈×C₁₇

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₇
prime radical	C₂×D₈×C₁₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄×Q₈×C₁₇ ◁ G

404 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 208 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1088

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2110);