Finite Group Databasebeta

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C2×D5×C11×C13⋊C3 #22575116

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C11×C13⋊C3
unambiguous semidirect productC5⋊(C22×C11×C13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C2×C11×C13⋊C3)
unambiguous semidirect product(C2×D5×C13)⋊(C3×C11)
unambiguous semidirect product(C2×D5×C11×C13)⋊C3

Splittings

Fitting, socleC2×C5×C11×C13 ⋊ C2×C3
derived, HallC5×C13 ⋊ C22×C3×C11
HallC2×D5×C11×C13 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C22
HallC5×C11×C13 ⋊ C22×C3
HallC2×D5×C13 ⋊ C3×C11
HallC5×C13⋊C3 ⋊ C22×C11
HallC11×C13 ⋊ C2×C3×D5
HallC5×C11 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×C3×D5×C11
SylowC5 ⋊ C22×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11D5×C13⋊C3
commutator, hypocenterC5×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

616 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D5×C11×C13⋊C3, C2×C3×D5×C11×C13⋊C3, C2×C11×D15×C13⋊C3
maximal normal subgroup ofC2×C3×D5×C11×C13⋊C3
maximal quotient ofC2×D5×C11×C13⋊C9, D3×D5×C11×C13⋊C3, C2×C3×D5×C11×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 88);