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D13×D165 #22575158

order8580
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD13×D165
unambiguous semidirect product(C3×D13)⋊D55
unambiguous semidirect product(C5×D13)⋊D33
unambiguous semidirect product(C11×D13)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C2×D11
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D15
HallC5×C13 ⋊ C2×D33
HallC5×C11 ⋊ D3×D13
HallC3×C13 ⋊ C2×D55
HallC3×C11 ⋊ D5×D13
HallC3×C5 ⋊ D11×D13
SylowC13 ⋊ C2×D165
SylowC11 ⋊ D13×D15
SylowC5 ⋊ D13×D33
SylowC3 ⋊ D13×D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C13C22
LCSG ▷ C3×C5×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

672 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×D495, D13⋊C3×D165, C3×D13×D165, …
maximal normal subgroup ofD13⋊C3×D165, C3×D13×D165
maximal quotient ofD13×D495, C3×D13×D165, D39⋊D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 130);