Finite Group Databasebeta

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D13×D555 #43274385

order28860
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD13×D555
unambiguous semidirect product(C3×D13)⋊D185
unambiguous semidirect product(C5×D13)⋊D111
unambiguous semidirect product(D13×C37)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C13×C37 ⋊ C22
HallC5×C13×C37 ⋊ C2×D3
HallC3×C13×C37 ⋊ C2×D5
HallC3×C5×C37 ⋊ C2×D13
HallC13×C37 ⋊ C2×D15
HallC3×C5×C13 ⋊ C2×D37
HallC5×C37 ⋊ D3×D13
HallC3×C37 ⋊ D5×D13
HallC5×C13 ⋊ C2×D111
HallC3×C13 ⋊ C2×D185
SylowC37 ⋊ D13×D15
HallC3×C5 ⋊ D13×D37
SylowC13 ⋊ C2×D555
SylowC5 ⋊ D13×D111
SylowC3 ⋊ D13×D185

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C37C22
LCSG ▷ C3×C5×C13×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7215

Conjugacy classes & character table

2232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 290);