Finite Group Databasebeta

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D3×D5×C11×C13 #22575163

order8580
automorphism?
homologyAbelianization (H1) = C22×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productD3×D5×C11×C13
unambiguous semidirect product(C5×D3)⋊(C2×C11×C13)
unambiguous semidirect product(C3×D5)⋊(C2×C11×C13)
unambiguous semidirect productD15⋊(C2×C11×C13)

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C22
derived, HallC3×C5 ⋊ C22×C11×C13
HallC5×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C22×C11
HallC3×C5×C11 ⋊ C22×C13
HallC5×C13 ⋊ C2×D3×C11
HallC5×C11 ⋊ C2×D3×C13
HallC3×C13 ⋊ C2×D5×C11
HallC3×C11 ⋊ C2×D5×C13
SylowC5 ⋊ C2×D3×C11×C13
SylowC3 ⋊ C2×D5×C11×C13

Subgroups

subgroupG/H
center, hypercenterC11×C13D3×D5
commutator, hypocenterC3×C5C22×C11×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C3×C5
UCSC1 ◁ C11×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×C11×C13×D9, D3×D5×C11×C13⋊C3, C3×D3×D5×C11×C13, …
maximal normal subgroup ofD3×D5×C11×C13⋊C3, C3×D3×D5×C11×C13
maximal quotient ofD5×C11×C13×D9, C3×D3×D5×C11×C13, D3×C11×C13×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 135);