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D13×#11925894 #44538181

order31460
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD13×#11925894

Splittings

Fitting, socle, derived, HallC112×C13 ⋊ C22×C5
HallC13×#10597244 ⋊ C22
HallD13×C11⋊D11 ⋊ C5
Hall#10597244 ⋊ C2×D13
SylowC112 ⋊ C2×C5×D13
SylowC13 ⋊ C2×#11925894

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC112×C13C22×C5
LCSG ▷ C112×C13
UCSC1

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 715

A minimal faithful permutation representation — 2 generators on 35 points:

(2,5,6,10,9,3,4,7,8,11)(13,17,18,16,21,14,15,22,19,20)(23,24,26,28,30,32,34,35,33,31,29,27,25);(1,2,5,8,6,9,11,7,10,4,3)(12,13,16,21,15,18,22,17,20,19,14)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 121);