C₁₃×#14676 #15701015

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

Aliases

direct product

C₁₃×#14676

Subgroups

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

1182 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 462 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) = 3328

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

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

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 7664);