C₂³×C₁₃×#123 #15748997

order	3328
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₃ · Schur multiplier (H₂) = C₂¹⁴

Aliases

C₂³×C₁₃×#123

	subgroup	G/H
center, socle	C₂⁵×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂⁴×D₄×C₁₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₃ ◁ G

15150 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1664

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

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

1456 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 55646);