C₂×C₁₃×#2867 #15722981

order	3328
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁷×C₄³

Aliases

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

8094 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 5 generators on 27 points:

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

1144 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 29630);