Finite Group Databasebeta

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C5×D3×C11×C53 #31775815

order17490
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C53 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C11×C53
unambiguous semidirect productC3⋊(C2×C5×C11×C53)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, SylowC3 ⋊ C2×C5×C11×C53
HallC3×C11×C53 ⋊ C2×C5
HallC3×C5×C53 ⋊ C2×C11
HallC3×C5×C11 ⋊ C2×C53
HallC3×C53 ⋊ C2×C5×C11
HallC3×C11 ⋊ C2×C5×C53
HallC3×C5 ⋊ C2×C11×C53

Subgroups

subgroupG/H
center, hypercenterC5×C11×C53D3
commutator, cosocle, hypocenterC3C2×C5×C11×C53
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C3
UCSC1 ◁ C5×C11×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

8745 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D53, C5×D3×D11×C53, C5×D3×D583, …
maximal normal subgroup ofC5×D3×C11×D53, C5×D3×D11×C53, C5×D3×D583, …
maximal quotient ofC5×C11×Dic3×C53, C2×C5×D3×C11×C53

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 10);