C₁₃×#14673 #15701012

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

direct product

C₁₃×#14673

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁶×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

2734 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 2734 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) = 832

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

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

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, 7661);