Finite Group Databasebeta

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C3×C5×D583 #31775810

order17490
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D583
unambiguous semidirect productC53⋊(C3×C5×D11)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC11×C53 ⋊ C2×C3×C5
HallC5×C11×C53 ⋊ C2×C3
HallC3×C11×C53 ⋊ C2×C5
HallC3×C5×C53 ⋊ D11
HallC5×C53 ⋊ C3×D11
HallC3×C5×C11 ⋊ D53
HallC3×C53 ⋊ C5×D11
HallC5×C11 ⋊ C3×D53
SylowC53 ⋊ C3×C5×D11
HallC3×C11 ⋊ C5×D53
SylowC11 ⋊ C3×C5×D53

Subgroups

subgroupG/H
center, hypercenterC3×C5D583
commutator, cosocle, hypocenterC11×C53C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C11×C53
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4395 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D11×D53, C3×D5×D583, C3×D55⋊D53, …
maximal normal subgroup ofC3×C5×D11×D53, C3×D5×D583, C3×D55⋊D53, …
maximal quotient ofC3×C5×Dic583, C2×C3×C5×D583

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 5);