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C7×(C181⋊C3)⋊C5 #34039604

order19005
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C181⋊C3)⋊C5
unambiguous semidirect product(C181⋊C3)⋊(C5×C7)
unambiguous semidirect product(C181⋊C5)⋊(C3×C7)
unambiguous semidirect product(C7×C181⋊C3)⋊C5

Splittings

Fitting, socle, HallC7×C181 ⋊ C3×C5
derived, SylowC181 ⋊ C3×C5×C7
HallC7×C181⋊C5 ⋊ C3
HallC7×C181⋊C3 ⋊ C5
HallC181⋊C5 ⋊ C3×C7
HallC181⋊C3 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC7(C181⋊C3)⋊C5
commutator, cosocle, hypocenterC181C3×C5×C7
FrattiniC1G
Fitting, socleC7×C181C3×C5
LCSG ▷ C181
UCSC1 ◁ C7

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1267

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×(C181⋊C3)⋊C5, C7×(D181⋊C3)⋊C5, D7×(C181⋊C3)⋊C5, …
maximal normal subgroup ofC2×C7×(C181⋊C3)⋊C5, C7×(D181⋊C3)⋊C5, D7×(C181⋊C3)⋊C5, …
maximal quotient ofC2×C7×(C181⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19005, 7);