C₂²×C₁₇×H(5,𝔽₂) #14526597

order	2176
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₇ · Schur multiplier (H₂) = C₂¹⁴

Aliases

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁶×C₁₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ G

6560 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 29 points:

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

1156 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 2323);