Finite Group Databasebeta

← Prev (#22575160) Next (#22575162) →

D15×D143 #22575161

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

Aliases

direct productD15×D143

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 ⋊ D3×D11
HallC5×C11 ⋊ D3×D13
HallC3×C13 ⋊ D5×D11
HallC3×C11 ⋊ D5×D13
HallC3×C5 ⋊ C2×D143
SylowC13 ⋊ D11×D15
SylowC11 ⋊ D13×D15
SylowC5 ⋊ D3×D143
SylowC3 ⋊ D5×D143

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

657 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD45×D143, D15×C11⋊(D13⋊C3), C3×D15×D143, …
maximal normal subgroup ofD15×C11⋊(D13⋊C3), C3×D15×D143
maximal quotient ofD45×D143, C3×D15×D143, #38788242, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 133);