C₁₃×#11524 #15697863

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11521
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11524

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
socle	C₂×C₁₃	#1464
prime radical	C₂×C₁₃×#41	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₄²×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

288 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 98 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)(14,15,18,24,19,23,34,40,20,25,33,41,17,22,31,39)(16,26,29,42,28,21,35,37,27,36,32,44,30,38,43,45);(14,16)(15,21)(17,30)(18,32)(19,28)(20,27)(22,26)(23,36)(24,37)(25,38)(29,33)(31,35)(34,43)(39,42)(40,44)(41,45);(15,22,25,23)(16,27)(18,33)(21,36,38,26)(24,40,41,39)(28,30)(31,34)(37,42,45,44)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4512);