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C5×D1419 #28381998

order14190
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1419
unambiguous semidirect productC3⋊(C5×D473)
unambiguous semidirect productC43⋊(C5×D33)

Splittings

Fitting, socle, HallC3×C5×C11×C43 ⋊ C2
derived, HallC3×C11×C43 ⋊ C2×C5
HallC5×C11×C43 ⋊ D3
HallC3×C5×C43 ⋊ D11
HallC11×C43 ⋊ C5×D3
HallC5×C43 ⋊ D33
HallC3×C5×C11 ⋊ D43
HallC3×C43 ⋊ C5×D11
HallC5×C11 ⋊ D129
SylowC43 ⋊ C5×D33
HallC3×C11 ⋊ C5×D43
HallC3×C5 ⋊ D473
SylowC11 ⋊ C5×D129
SylowC3 ⋊ C5×D473

Subgroups

subgroupG/H
center, hypercenterC5D1419
commutator, cosocle, hypocenterC3×C11×C43C2×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C43C2
LCSG ▷ C3×C11×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7095

Conjugacy classes & character table

3555 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D33×D43, C5×D11×D129, C5×D3×D473, …
maximal normal subgroup ofC5×D33×D43, C5×D11×D129, C5×D3×D473, …
maximal quotient ofC5×Dic1419, C2×C5×D1419

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 15);