Finite Group Databasebeta

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C11×D15×C53 #31775819

order17490
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C11×C53 · Schur multiplier (H2) = C1

Aliases

direct productC11×D15×C53
unambiguous semidirect productC3⋊(D5×C11×C53)
unambiguous semidirect productC5⋊(D3×C11×C53)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC3×C5 ⋊ C2×C11×C53
HallC5×C11×C53 ⋊ D3
HallC3×C11×C53 ⋊ D5
HallC3×C5×C53 ⋊ C2×C11
HallC5×C53 ⋊ D3×C11
HallC3×C5×C11 ⋊ C2×C53
HallC3×C53 ⋊ D5×C11
HallC5×C11 ⋊ D3×C53
HallC3×C11 ⋊ D5×C53
SylowC5 ⋊ D3×C11×C53
SylowC3 ⋊ D5×C11×C53

Subgroups

subgroupG/H
center, hypercenterC11×C53D15
commutator, cosocle, hypocenterC3×C5C2×C11×C53
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C3×C5
UCSC1 ◁ C11×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

5247 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D15×D53, D11×D15×C53, D15×D583, …
maximal normal subgroup ofC11×D15×D53, D11×D15×C53, D15×D583, …
maximal quotient ofC11×C53×Dic15, C2×C11×D15×C53

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 14);