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C3×D2915 #31775814

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

Aliases

direct productC3×D2915
unambiguous semidirect productC5⋊(C3×D583)
unambiguous semidirect productC11⋊(C3×D265)
unambiguous semidirect productC53⋊(C3×D55)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC5×C11×C53 ⋊ C2×C3
HallC3×C11×C53 ⋊ D5
HallC3×C5×C53 ⋊ D11
HallC11×C53 ⋊ C3×D5
HallC5×C53 ⋊ C3×D11
HallC3×C5×C11 ⋊ D53
HallC3×C53 ⋊ D55
HallC5×C11 ⋊ C3×D53
SylowC53 ⋊ C3×D55
HallC3×C11 ⋊ D265
HallC3×C5 ⋊ D583
SylowC11 ⋊ C3×D265
SylowC5 ⋊ C3×D583

Subgroups

subgroupG/H
center, hypercenterC3D2915
commutator, cosocle, hypocenterC5×C11×C53C2×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C5×C11×C53
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4377 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D53×D55, C3×D11×D265, C3×D5×D583, …
maximal normal subgroup ofC3×D53×D55, C3×D11×D265, C3×D5×D583, …
maximal quotient ofC3×Dic2915, C2×C3×D2915

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 9);