Finite Group Databasebeta

← Prev (#27134220) Next (#27134222) →

C5×C3⋊(#4223⋊C5) #27134221

order12300
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C3⋊(#4223⋊C5)
unambiguous semidirect productC3⋊(C5×#4223⋊C5)
unambiguous semidirect product(C3⋊#4223)⋊C52
unambiguous semidirect product(C5×C3⋊#4223)⋊C5

Splittings

Fitting, socleC3×C5×C41 ⋊ C4×C5
derived, HallC3×C41 ⋊ C4×C52
HallC3×C5×C41⋊C5 ⋊ C4
HallC5×C41⋊C5 ⋊ Dic3
HallC3⋊#4223 ⋊ C52
SylowC41 ⋊ C52×Dic3
SylowC3 ⋊ C5×#4223⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(#4223⋊C5)
commutator, hypocenterC3×C41C4×C52
FrattiniC1G
Fitting, socleC3×C5×C41C4×C5
prime radicalC3×C5×D41⋊C5C2
cosocleC3×D41C2×C52
LCSG ▷ C3×C41
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C9⋊(#4223⋊C5), C3×C5×C3⋊(#4223⋊C5), C5×C3⋊(C3⋊(#4223⋊C5))
maximal normal subgroup ofC3×C5×C3⋊(#4223⋊C5)
maximal quotient ofC5×C9⋊(#4223⋊C5), C3×C5×C3⋊(#4223⋊C5), C5×C3⋊(C3⋊(#4223⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12300, 83);