C₂²×D₄²×C₁₇ #16920439

order	4352
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₇ · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂²×D₄²×C₁₇

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

20038 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 1088

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);(5,6,7,8);(6,8);(9,10,11,12);(10,12)

1700 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 55683);