C₁₃×#12779 #15699118

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12778
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#12779

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1790
commutator	C₂×Q₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

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

normal subgroups only

This group has 732 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)(16,26,29,40)(17,23,18,31)(19,24)(20,25)(21,27)(22,30,39,33)(28,42,45,35)(32,37)(34,38)(36,43)(41,44);(14,16,20,29)(15,21,25,37)(17,27,18,32)(19,28,34,45)(22,35,39,42)(23,40,31,26)(24,41,38,36)(30,43,33,44);(14,17)(15,22)(16,27)(18,20)(19,33)(21,35)(23,38)(24,31)(25,39)(26,41)(28,44)(29,32)(30,34)(36,40)(37,42)(43,45)

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, 5767);