C₁₃×#11854 #15698193

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11757
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11854

Subgroups

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

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

normal subgroups only

This group has 412 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) = 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)(16,22,24,29)(17,21)(18,20)(19,23,27,25)(26,28)(30,31,34,39,35,38,33,37)(32,40,41,45,42,36,43,44);(14,16)(15,19)(17,25)(18,24)(20,27)(21,29)(22,28)(23,26)(30,32,35,42)(31,36,38,40)(33,43,34,41)(37,44,39,45);(15,20)(19,27)(21,28)(22,29)(30,33,35,34)(31,37,38,39)(32,41,42,43)(36,44,40,45)

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, 4842);