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C13×#1201 #13095642

order1560
isoclinismisoclinic class of #1201
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×#1201

Splittings

HallC3×C5×C13 ⋊ D4
HallC5×C13 ⋊ #67
HallC3×C13 ⋊ C22⋊D5
HallC3×C5 ⋊ D4×C13
SylowC5 ⋊ C13×#67
SylowC3 ⋊ C13×C22⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C13D3×D5
commutator, cosocleC2×C3×C5C22×C13
FrattiniC2D3×D5×C13
Fitting, socleC2×C3×C5×C13C22
hypocenterC3×C5D4×C13
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 780

A minimal faithful permutation representation — 2 generators on 25 points:

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

Conjugacy classes & character table

273 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 78);