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C3×C13×D20 #13095679

order1560
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC3×C13×D20
unambiguous semidirect productC4⋊(C3×D5×C13)

Splittings

FittingC3×C4×C5×C13 ⋊ C2
HallC3×C5×C13 ⋊ D4
HallC5×C13 ⋊ C3×D4
HallC3×C5 ⋊ D4×C13
SylowC5 ⋊ C3×D4×C13

Subgroups

subgroupG/H
centerC2×C3×C13C2×D5
commutator, cosocleC2×C5C22×C3×C13
FrattiniC2C2×C3×D5×C13
FittingC3×C4×C5×C13C2
socleC2×C3×C5×C13C22
hypercenterC3×C4×C13D5
hypocenterC5C3×D4×C13
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C13 ◁ C3×C4×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)(4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20)(21,22,23,24,25);(18,20)(22,25)(23,24)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 115);