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C2×C3×C3⋊(D41⋊C5) #20301603

order7380
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C3⋊(D41⋊C5)
unambiguous semidirect product(C2×C3)⋊(C3×D41⋊C5)
unambiguous semidirect product(C2×C41⋊C5)⋊(C3×D3)
unambiguous semidirect product(C2×D123)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D123)⋊C5

Splittings

Fitting, socleC2×C32×C41 ⋊ C2×C5
derivedC3×C41 ⋊ C22×C3×C5
HallC32×C41⋊C5 ⋊ C22
HallC2×C3×D123 ⋊ C5
HallC32×C41 ⋊ C22×C5
HallC41⋊C5 ⋊ C2×C3×D3
SylowC41 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D41⋊C5)
commutator, hypocenterC3×C41C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C41C2×C5
LCSG ▷ C3×C41
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×C3⋊(D41⋊C5), C2×C3×C5×C3⋊(D41⋊C5), C2×C3×C3⋊(C5⋊(D41⋊C5))
maximal normal subgroup ofC2×C3×C5×C3⋊(D41⋊C5)
maximal quotient ofC2×C3×C3⋊(D41⋊C25), C3×D5×C3⋊(D41⋊C5), C2×C3×C5×C3⋊(D41⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 81);