C₁₃×#11868 #15698207

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11867
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#11868

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1519
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₁₃×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

396 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 110 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)(16,26)(17,31,34,20)(18,23)(19,25)(21,27)(22,32,36,44)(24,28)(29,38,33,37)(30,39)(35,45,41,42)(40,43);(15,20)(16,27)(17,32)(18,28)(21,37)(22,24)(23,36)(25,31)(26,41)(29,33)(30,43)(34,44)(35,39)(38,40);(14,16,28,43,19,30,18,27)(15,21,23,39,25,40,24,26)(17,33,44,42,34,29,32,45)(20,35,22,37,31,41,36,38)

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, 4856);