C₁₃×#12873 #15699212

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12873
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12873

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1823
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

380 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 138 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)(16,25,27,20)(17,29)(18,33)(19,22)(21,26,38,43)(23,31)(24,35)(28,37,34,41)(30,39,44,36)(32,42)(40,45);(14,16)(15,20)(17,26)(18,28)(19,27)(21,29)(22,25)(23,36)(24,37)(30,31)(32,43)(33,41)(34,35)(38,42)(39,40)(44,45);(14,16)(15,21,22,38)(17,30)(18,34)(19,27)(20,29,25,42)(23,41,40,37)(24,36,33,39)(26,31)(28,35)(32,44)(43,45)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5861);