C₁₃×#11991 #15698330

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11989
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11991

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1551
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#540	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 280 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)(14,15,17,23,30,20,29,33,19,24,32,39,18,22,31,38)(16,25,27,40,42,36,43,44,26,37,41,45,28,21,34,35);(15,20)(17,29)(18,30)(21,25)(22,24)(23,39)(27,43)(28,42)(31,32)(34,41)(35,44)(36,37);(14,16)(15,21,24,36)(17,27)(18,28)(19,26)(20,25,22,37)(23,35,39,44)(29,43)(30,42)(31,34)(32,41)(33,40,38,45)

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, 4979);