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C2×C13×#3532 #15749057

order3328
nilpotency class2
isoclinismisoclinic class of #3532
automorphism?
homologyAbelianization (H1) = C26×C13 · Schur multiplier (H2) = C213

Aliases

direct productC2×C13×#3532

Subgroups

subgroupG/H
center, socleC23×C13C25
commutator, Frattini, cosocleC22C26×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

9542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 416

A minimal faithful permutation representation — 6 generators on 31 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4)(5,11)(6,10)(7,9)(8,13)(12,15)(14,17)(16,18);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,18)(15,17);(4,9)(5,12)(10,17)(13,18);(4,9)(5,13)(8,15)(10,17)(11,16)(12,18);(4,10)(8,11)(9,17)(15,16)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 55706);