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D39⋊D55 #22575174

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

Aliases

unambiguous semidirect productD39⋊D55

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 ⋊ D3×D5
HallC5×C13 ⋊ D3×D11
HallC5×C11 ⋊ D3×D13
HallC3×C13 ⋊ C2×D55
HallC3×C11 ⋊ D5×D13
HallC3×C5 ⋊ D11×D13
SylowC13 ⋊ D3×D55
SylowC11 ⋊ D15⋊D13
SylowC5 ⋊ D33⋊D13
SylowC3 ⋊ D13×D55

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|d^a=d^4,e^a=e^10,f^a=f^12,c^b=c^2,d^b=d^4,e^b=e^10

Conjugacy classes & character table

591 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD117⋊D55, (C3⋊(D13⋊C3))⋊D55, C3×D39⋊D55, …
maximal normal subgroup of(C3⋊(D13⋊C3))⋊D55, C3×D39⋊D55
maximal quotient ofD117⋊D55, C3×D39⋊D55, D39⋊D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 146);