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C11×D13×D15 #22575156

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

Aliases

direct productC11×D13×D15
unambiguous semidirect product(C3×D13)⋊(D5×C11)
unambiguous semidirect product(C5×D13)⋊(D3×C11)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC11D13×D15
commutator, hypocenterC3×C5×C13C22×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

792 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×D13×D45, C11×D15×D13⋊C3, C3×C11×D13×D15, …
maximal normal subgroup ofC11×D15×D13⋊C3, C3×C11×D13×D15
maximal quotient ofC11×D13×D45, C3×C11×D13×D15, C11×D39⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 128);