Finite Group Databasebeta

← Prev (#26015301) Next (#26015303) →

C5×(C151⋊C3)⋊C5 #26015302

order11325
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×(C151⋊C3)⋊C5
unambiguous semidirect product(C151⋊C3)⋊C52
unambiguous semidirect product(C151⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×C151⋊C3)⋊C5
unambiguous semidirect product(C5×C151⋊C5)⋊C3

Splittings

Fitting, socleC5×C151 ⋊ C3×C5
derived, SylowC151 ⋊ C3×C52
HallC5×C151⋊C5 ⋊ C3
HallC151⋊C3 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC5(C151⋊C3)⋊C5
commutator, cosocle, hypocenterC151C3×C52
FrattiniC1G
Fitting, socleC5×C151C3×C5
LCSG ▷ C151
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×(D151⋊C3)⋊C5, C5⋊((D151⋊C3)⋊C5), D5×(C151⋊C3)⋊C5, …
maximal normal subgroup ofC5×(D151⋊C3)⋊C5, C5⋊((D151⋊C3)⋊C5), D5×(C151⋊C3)⋊C5, …
maximal quotient ofC2×C5×(C151⋊C3)⋊C5, C5×(C151⋊C5)⋊C9, C3×C5×(C151⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11325, 8);