Finite Group Databasebeta

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C11×#13918 #14591111

order2816
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25×C4

Aliases

direct productC11×#13918

Subgroups

subgroupG/H
center, socle, prime radicalC24×C11C24
commutatorC23C23×C4×C11
Frattini, cosocleC24C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

1426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 2816

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

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 6906);