C₁₃×#11912 #15698251

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11912
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11912

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1530
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	#97	C₂³×C₁₃
prime radical	C₁₃×#540	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

284 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 94 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)(14,15,17,23,18,20,32,34,19,24,31,40,33,22,29,39)(16,25,27,42,28,37,44,41,26,38,30,45,43,21,35,36);(15,20)(17,29)(18,33)(21,25)(22,24)(23,40)(27,35)(28,43)(30,44)(31,32)(36,41)(37,38);(14,16)(15,21,24,37)(17,30)(18,28)(19,26)(20,25,22,38)(23,41,40,36)(27,31)(29,44)(32,35)(33,43)(34,45,39,42)

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, 4900);