C₂⁴×Q₈×C₁₇ #14526595

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₇ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂⁴×Q₈×C₁₇

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₁₇	C₂²
commutator, Frattini, cosocle	C₂	C₂⁶×C₁₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₇ ◁ G

6264 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 6 generators on 33 points:

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

1360 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2321);