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C2×C13×#1600 #15704451

order3328
nilpotency class3
isoclinismisoclinic class of #1595
automorphism?
homologyAbelianization (H1) = C24×C13 · Schur multiplier (H2) = C26

Aliases

direct productC2×C13×#1600

Subgroups

subgroupG/H
center, socleC23×C13#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C23×C4×C13 ◁ G

1716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 11100);