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C3⋊D3×D41⋊C5 #20301594

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

Aliases

direct productC3⋊D3×D41⋊C5
unambiguous semidirect productD41⋊(C5×C3⋊D3)
unambiguous semidirect product(C3×D41⋊C5)⋊D3
unambiguous semidirect product(C3⋊D3×D41)⋊C5

Splittings

Fitting, socle, derived, HallC32×C41 ⋊ C22×C5
HallC32×C41⋊C5 ⋊ C22
HallC3⋊D3×D41 ⋊ C5
HallC41⋊C5 ⋊ C2×C3⋊D3
SylowC41 ⋊ C2×C5×C3⋊D3
SylowC32 ⋊ C2×D41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C41C22×C5
LCSG ▷ C32×C41
UCSC1

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C3⋊D3×D41⋊C5, C3⋊D15×D41⋊C5, C3⋊D3×C5⋊(D41⋊C5), …
maximal normal subgroup ofC5×C3⋊D3×D41⋊C5, C3⋊D3×#4223⋊C5, D32×D41⋊C5, …
maximal quotient ofC3⋊D3×D41⋊C25, C5×C3⋊D3×D41⋊C5, C3⋊D15×D41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 72);