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C2×C3×(C211⋊C3)⋊C5 #34039488

order18990
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×(C211⋊C3)⋊C5
unambiguous semidirect product(C2×C211⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×C211⋊C5)⋊C32
unambiguous semidirect product(C2×C3×C211⋊C3)⋊C5
unambiguous semidirect product(C2×C3×C211⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C211 ⋊ C3×C5
derived, SylowC211 ⋊ C2×C32×C5
HallC2×C3×C211⋊C3 ⋊ C5
HallC2×C211⋊C5 ⋊ C32
HallC3×C211⋊C3 ⋊ C2×C5
HallC211⋊C5 ⋊ C2×C32
HallC2×C211 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3(C211⋊C3)⋊C5
commutator, cosocle, hypocenterC211C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C211C3×C5
LCSG ▷ C211
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1266

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C211⋊C3)⋊C4)⋊C5, C3⋊(((C211⋊C3)⋊C4)⋊C5), Dic3×(C211⋊C3)⋊C5, …
maximal normal subgroup ofC3×((C211⋊C3)⋊C4)⋊C5, C3⋊(((C211⋊C3)⋊C4)⋊C5), Dic3×(C211⋊C3)⋊C5, …
maximal quotient ofC3×C4×(C211⋊C3)⋊C5, C22×C3×(C211⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18990, 23);