C₁₃×#21683 #15708022

order	3328
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#21683

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₁₃×#2397	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

1266 conjugacy classes of subgroups; only the 406 normal subgroups are shown.

normal subgroups only

This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 406 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,21)(22,23,26,30,27,25,29,34)(24,28,33,36,31,32,35,37);(14,15,16,17)(22,24)(23,28)(25,32)(26,33)(27,31)(29,35)(30,36)(34,37);(18,19,20,21)(24,31)(28,32)(33,35)(36,37);(22,25,26,34,27,23,29,30)(24,32,33,37,31,28,35,36)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 14671);