C₁₃×#11836 #15698175

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11836

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1514
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₁₃×#469	C₂²
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

286 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26,28,43)(17,31,33,38)(18,24)(19,22)(20,25)(21,27)(23,34,40,35)(29,39,30,42)(32,41)(36,45)(37,44);(14,16)(15,21)(17,32)(18,30)(19,29)(20,28)(22,36)(23,39)(24,41)(25,37)(26,31)(27,35)(33,45)(34,44)(38,43)(40,42);(15,22,25,24)(17,33)(21,36,37,41)(23,31,40,38)(26,42,43,39)(27,44)(32,45)(34,35)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4824);