C₁₃×#12708 #15699047

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12707
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#12708

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1781
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×D₄	C₂³×C₁₃
prime radical	C₁₃×#3487	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂³×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

1002 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 146 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)(16,24,27,38)(17,21)(18,30,33,22)(19,23)(20,26)(25,41,43,40)(28,39,32,36)(29,37)(31,35)(34,42)(44,45);(14,16)(15,20)(17,25)(18,31)(19,27)(21,34)(22,38)(23,35)(24,30)(26,33)(28,44)(29,43)(32,42)(36,40)(37,45)(39,41);(14,17,19,29)(15,21,23,37)(16,25,27,43)(18,32,33,28)(20,34,35,45)(22,39,30,36)(24,40,38,41)(26,44,31,42)

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, 5696);