Finite Group Databasebeta

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C3×C11×D265 #31775812

order17490
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D265
unambiguous semidirect productC5⋊(C3×C11×D53)
unambiguous semidirect productC53⋊(C3×D5×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC5×C53 ⋊ C2×C3×C11
HallC5×C11×C53 ⋊ C2×C3
HallC3×C11×C53 ⋊ D5
HallC3×C5×C53 ⋊ C2×C11
HallC11×C53 ⋊ C3×D5
HallC3×C5×C11 ⋊ D53
HallC3×C53 ⋊ D5×C11
HallC5×C11 ⋊ C3×D53
SylowC53 ⋊ C3×D5×C11
HallC3×C5 ⋊ C11×D53
SylowC5 ⋊ C3×C11×D53

Subgroups

subgroupG/H
center, hypercenterC3×C11D265
commutator, cosocle, hypocenterC5×C53C2×C3×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C5×C53
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4422 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×#11761505, C3×C11×#11761506, C3×C11⋊#11761505, …
maximal normal subgroup ofC3×C11×#11761505, C3×C11×#11761506, C3×C11⋊#11761505, …
maximal quotient ofC3×C11×Dic265, C2×C3×C11×D265

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 7);