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C3×C5×D52 #13095674

order1560
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×D52
unambiguous semidirect productC4⋊(C3×C5×D13)

Splittings

FittingC3×C4×C5×C13 ⋊ C2
HallC3×C5×C13 ⋊ D4
HallC5×C13 ⋊ C3×D4
HallC3×C13 ⋊ C5×D4
SylowC13 ⋊ C3×C5×D4

Subgroups

subgroupG/H
centerC2×C3×C5C2×D13
commutator, cosocleC2×C13C22×C3×C5
FrattiniC2C2×C3×C5×D13
FittingC3×C4×C5×C13C2
socleC2×C3×C5×C13C22
hypercenterC3×C4×C5D13
hypocenterC13C3×C5×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C3×C5 ◁ C3×C4×C5

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);(10,12)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1560, 110);