D₄×#41×C₁₇ #14526474

order	2176
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₇ · Schur multiplier (H₂) = C₂⁹

Aliases

D₄×#41×C₁₇

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ G

1648 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 5 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2200);