Finite Group Databasebeta

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C5×D1749 #31775818

order17490
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1749
unambiguous semidirect productC3⋊(C5×D583)
unambiguous semidirect productC53⋊(C5×D33)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC3×C11×C53 ⋊ C2×C5
HallC5×C11×C53 ⋊ D3
HallC3×C5×C53 ⋊ D11
HallC11×C53 ⋊ C5×D3
HallC5×C53 ⋊ D33
HallC3×C5×C11 ⋊ D53
HallC3×C53 ⋊ C5×D11
HallC5×C11 ⋊ D159
SylowC53 ⋊ C5×D33
HallC3×C11 ⋊ C5×D53
HallC3×C5 ⋊ D583
SylowC11 ⋊ C5×D159
SylowC3 ⋊ C5×D583

Subgroups

subgroupG/H
center, hypercenterC5D1749
commutator, cosocle, hypocenterC3×C11×C53C2×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C3×C11×C53
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4380 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D33×D53, C5×D11×D159, C5×D3×D583, …
maximal normal subgroup ofC5×D33×D53, C5×D11×D159, C5×D3×D583, …
maximal quotient ofC5×Dic1749, C2×C5×D1749

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 13);