Finite Group Databasebeta

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C3×C53×D55 #31775813

order17490
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1

Aliases

direct productC3×C53×D55
unambiguous semidirect productC5⋊(C3×D11×C53)
unambiguous semidirect productC11⋊(C3×D5×C53)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, HallC5×C11 ⋊ C2×C3×C53
HallC5×C11×C53 ⋊ C2×C3
HallC3×C11×C53 ⋊ D5
HallC3×C5×C53 ⋊ D11
HallC11×C53 ⋊ C3×D5
HallC5×C53 ⋊ C3×D11
HallC3×C5×C11 ⋊ C2×C53
HallC3×C11 ⋊ D5×C53
HallC3×C5 ⋊ D11×C53
SylowC11 ⋊ C3×D5×C53
SylowC5 ⋊ C3×D11×C53

Subgroups

subgroupG/H
center, hypercenterC3×C53D55
commutator, cosocle, hypocenterC5×C11C2×C3×C53
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C5×C11
UCSC1 ◁ C3×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

4611 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D53×D55, C3×D5×D11×C53, C3×D55⋊D53, …
maximal normal subgroup ofC3×D53×D55, C3×D5×D11×C53, C3×D55⋊D53, …
maximal quotient ofC3×C53×Dic55, C2×C3×C53×D55

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 8);