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C3×C3⋊(Dic41⋊C5) #20301573

order7380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(Dic41⋊C5)
unambiguous semidirect productC3⋊(C3×Dic41⋊C5)
unambiguous semidirect productDic123⋊(C3×C5)
unambiguous semidirect product(C3×Dic123)⋊C5

Splittings

derivedC3×C41 ⋊ C3×C4×C5
HallC32×C41⋊C5 ⋊ C4
HallC3×Dic123 ⋊ C5
HallC32×C41 ⋊ C4×C5
HallC41⋊C5 ⋊ C3×Dic3
SylowC41 ⋊ C3×C5×Dic3
SylowC32 ⋊ Dic41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D41⋊C5)
commutator, hypocenterC3×C41C3×C4×C5
FrattiniC2C3×C3⋊(D41⋊C5)
Fitting, socleC2×C32×C41C2×C5
LCSG ▷ C3×C41
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C3⋊(Dic41⋊C5), C3×C3⋊(Dic205⋊C5), C3×C3⋊(#11717963⋊C5)
maximal normal subgroup ofC3×C5×C3⋊(Dic41⋊C5)
maximal quotient ofC3×C3⋊(Dic41⋊C25), C3×C5×C3⋊(Dic41⋊C5), C3×C3⋊(Dic205⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 51);