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D143⋊D15 #22575162

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

Aliases

unambiguous semidirect productD143⋊D15

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 ⋊ D11×D13
SylowC13 ⋊ D11×D15
SylowC11 ⋊ D13×D15
SylowC5 ⋊ D33⋊D13
SylowC3 ⋊ D55⋊D13

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 →

Presentation

Polycyclic presentation:

2^2,3,5,11,13|e^a=e^10,f^a=f^12,c^b=c^2,d^b=d^4,e^b=e^10

Conjugacy classes & character table

567 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD143⋊D45, (C11⋊(D13⋊C3))⋊D15, C3×D143⋊D15, …
maximal normal subgroup of(C11⋊(D13⋊C3))⋊D15, C3×D143⋊D15
maximal quotient ofD143⋊D45, C3×D143⋊D15, #38788243, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 134);