Finite Group Databasebeta

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C3×D5×C13×D11 #22575135

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C13×D11
unambiguous semidirect product(D5×C11)⋊(C2×C3×C13)
unambiguous semidirect product(C5×D11)⋊(C2×C3×C13)
unambiguous semidirect productD55⋊(C2×C3×C13)

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C22
derived, HallC5×C11 ⋊ C22×C3×C13
HallC5×C11×C13 ⋊ C22×C3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C2×D11
HallC3×C5×C11 ⋊ C22×C13
HallC11×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×C3×D11
HallC3×C11 ⋊ C2×D5×C13
HallC3×C5 ⋊ C2×C13×D11
SylowC11 ⋊ C2×C3×D5×C13
SylowC5 ⋊ C2×C3×C13×D11

Subgroups

subgroupG/H
center, hypercenterC3×C13D5×D11
commutator, hypocenterC5×C11C22×C3×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C5×C11
UCSC1 ◁ C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×D11×C13⋊C9, C9×D5×C13×D11, C3×D5×D11×C13⋊C3, …
maximal normal subgroup ofD5×D11×C13⋊C9, C9×D5×C13×D11, C3×D5×D11×C13⋊C3, …
maximal quotient ofC9×D5×C13×D11, C32×D5×C13×D11, C3×C13×D11×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 107);