C₁₃×#11543 #15697882

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11543

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	C₂×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂⁴×C₁₃ ◁ C₂²×C₁₃×C₂²⋊C₄ ◁ G

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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)(14,15,17,22,18,23,29,37)(16,24,26,36,25,38,39,45)(19,21,28,34,30,35,41,44)(20,31,33,40,32,42,43,27);(14,16,19,27)(15,20,21,24)(17,26,28,31)(18,25,30,40)(22,36,34,33)(23,32,35,38)(29,39,41,42)(37,45,44,43);(16,25)(20,32)(24,38)(26,39)(27,40)(31,42)(33,43)(36,45)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4531);