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D55⋊D57 #27160088

order12540
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD55⋊D57

Splittings

Fitting, socle, derived, HallC3×C5×C11×C19 ⋊ C22
HallC5×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D11
HallC11×C19 ⋊ D3×D5
HallC3×C5×C11 ⋊ C2×D19
HallC5×C19 ⋊ D3×D11
HallC3×C19 ⋊ D5×D11
HallC5×C11 ⋊ C2×D57
HallC3×C11 ⋊ D5×D19
SylowC19 ⋊ D15⋊D11
HallC3×C5 ⋊ D11×D19
SylowC11 ⋊ D5×D57
SylowC5 ⋊ D11×D57
SylowC3 ⋊ D55⋊D19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C19C22
LCSG ▷ C3×C5×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,5,11,19|c^a=c^2,e^a=e^10,f^a=f^18,d^b=d^4,e^b=e^10

Conjugacy classes & character table

840 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD55⋊D171, D55⋊(C3⋊(D19⋊C3)), C3×D55⋊D57, …
maximal normal subgroup ofD55⋊(C3⋊(D19⋊C3)), C3×D55⋊D57
maximal quotient ofD55⋊D171, C3×D55⋊D57, #49178721, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 118);