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C5×D1463 #28410693

order14630
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1463
unambiguous semidirect productC7⋊(C5×D209)
unambiguous semidirect productC19⋊(C5×D77)

Splittings

Fitting, socle, HallC5×C7×C11×C19 ⋊ C2
derived, HallC7×C11×C19 ⋊ C2×C5
HallC5×C11×C19 ⋊ D7
HallC5×C7×C19 ⋊ D11
HallC5×C7×C11 ⋊ D19
HallC11×C19 ⋊ C5×D7
HallC7×C19 ⋊ C5×D11
HallC5×C19 ⋊ D77
HallC7×C11 ⋊ C5×D19
HallC5×C11 ⋊ D133
HallC5×C7 ⋊ D209
SylowC19 ⋊ C5×D77
SylowC11 ⋊ C5×D133
SylowC7 ⋊ C5×D209

Subgroups

subgroupG/H
center, hypercenterC5D1463
commutator, cosocle, hypocenterC7×C11×C19C2×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C19C2
LCSG ▷ C7×C11×C19
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7315

Conjugacy classes & character table

3665 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D19×D77, C5×D11×D133, C5×D7×D209, …
maximal normal subgroup ofC5×D19×D77, C5×D11×D133, C5×D7×D209, …
maximal quotient ofC5×Dic1463, C2×C5×D1463

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14630, 9);