Finite Group Databasebeta

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C5×C53×D33 #31775817

order17490
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C2×C5×C53 · Schur multiplier (H2) = C1

Aliases

direct productC5×C53×D33
unambiguous semidirect productC3⋊(C5×D11×C53)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC3×C11 ⋊ C2×C5×C53
HallC5×C11×C53 ⋊ D3
HallC3×C11×C53 ⋊ C2×C5
HallC3×C5×C53 ⋊ D11
HallC11×C53 ⋊ C5×D3
HallC3×C5×C11 ⋊ C2×C53
HallC3×C53 ⋊ C5×D11
HallC5×C11 ⋊ D3×C53
HallC3×C5 ⋊ D11×C53
SylowC11 ⋊ C5×D3×C53
SylowC3 ⋊ C5×D11×C53

Subgroups

subgroupG/H
center, hypercenterC5×C53D33
commutator, cosocle, hypocenterC3×C11C2×C5×C53
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C3×C11
UCSC1 ◁ C5×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4770 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D33×D53, C5×D3×D11×C53, C5×D33⋊D53, …
maximal normal subgroup ofC5×D33×D53, C5×D3×D11×C53, C5×D33⋊D53, …
maximal quotient ofC5×C53×Dic33, C2×C5×C53×D33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 12);