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C13×#1200 #13095641

order1560
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×#1200

Splittings

derived, HallC3×C5 ⋊ C2×C4×C13
HallC3×C5×C13 ⋊ C2×C4
HallC5×C13 ⋊ C4×D3
HallC3×C13 ⋊ C4×D5
SylowC5 ⋊ C4×D3×C13
SylowC3 ⋊ C4×D5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D3×D5
commutator, hypocenterC3×C5C2×C4×C13
FrattiniC2D3×D5×C13
Fitting, socleC2×C3×C5×C13C22
prime radicalC2×C13×D15C2
cosocleC2×C3×C5C22×C13
LCSG ▷ 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)(22,24,25,23);(15,16)(17,18)(19,20,21)(22,23,25,24)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 77);