Finite Group Databasebeta

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C3×C5×C121⋊C5 #22583758

order9075
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C121⋊C5
unambiguous semidirect productC121⋊(C3×C52)
unambiguous semidirect product(C3×C121)⋊C52
unambiguous semidirect product(C5×C121)⋊(C3×C5)
unambiguous semidirect product(C3×C5×C121)⋊C5

Splittings

FittingC3×C5×C121 ⋊ C5
derived, SylowC121 ⋊ C3×C52
HallC3×C121 ⋊ C52

Subgroups

subgroupG/H
center, hypercenterC3×C5C121⋊C5
commutator, hypocenterC121C3×C52
FrattiniC11C3×C5×C11⋊C5
FittingC3×C5×C121C5
socleC3×C5×C11C11⋊C5
LCSG ▷ C121
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

435 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D121⋊C5, C3×D5×C121⋊C5, C3×C5⋊(D121⋊C5), …
maximal normal subgroup ofC3×C5×D121⋊C5, C3×D5×C121⋊C5, C3×C5⋊(D121⋊C5), …
maximal quotient ofC2×C3×C5×C121⋊C5, C5×C9×C121⋊C5, C32×C5×C121⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9075, 4);