C₁₃×#9450 #15695789

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9443
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9450

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

424 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 832

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)(16,23,24,27)(17,20,25,26)(18,21)(19,22)(28,29)(30,31,34,39,35,38,33,37)(32,36,40,43,41,44,42,45);(14,16,18,26,19,24,28,20)(15,17,21,27,22,25,29,23)(30,32,33,40,35,41,34,42)(31,36,39,45,38,44,37,43);(14,17)(15,20)(16,21)(18,27)(19,25)(22,26)(23,28)(24,29)(30,33,35,34)(31,37,38,39)(32,40,41,42)(36,43,44,45)

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, 2438);