C₁₃×#11870 #15698209

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11867
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#11870

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1519
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₁₃×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

392 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 110 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)(14,15,18,24,20,25,19,35)(16,26,27,40,30,43,29,22)(17,21,31,23,34,38,33,37)(28,41,45,42,32,39,44,36);(15,21)(16,27)(17,31)(18,19)(22,39)(23,24)(25,38)(26,36)(29,30)(33,34)(35,37)(40,41)(42,43)(44,45);(14,16,19,29,20,30,18,27)(15,22,24,26,25,40,35,43)(17,32,31,44,34,28,33,45)(21,36,37,39,38,42,23,41)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4858);