C₂³×C₁₇×#121 #16920400

order	4352
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₇ · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂³×C₁₇×#121

	subgroup	G/H
center, socle	C₂⁵×C₁₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₇ ◁ G

19998 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 6 generators on 31 points:

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

1904 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 55644);