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C2×C3⋊(C3⋊(D41⋊C5)) #20301605

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

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×C3⋊D123)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C3⋊(D41⋊C5))
commutator, hypocenterC32×C41C22×C5
FrattiniC1G
Fitting, socleC2×C32×C41C2×C5
LCSG ▷ C32×C41
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C3⋊(C3⋊(D41⋊C5)), C2×C5×C3⋊(C3⋊(D41⋊C5)), C2×C3⋊(C3⋊(C5⋊(D41⋊C5)))
maximal normal subgroup ofC2×C5×C3⋊(C3⋊(D41⋊C5))
maximal quotient ofC2×C3⋊(C3⋊(D41⋊C25)), D5×C3⋊(C3⋊(D41⋊C5)), C2×C5×C3⋊(C3⋊(D41⋊C5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 83);