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C41×(C3⋊D3)⋊D5 #20301646

order7380
isoclinismisoclinic class of (C3⋊D3)⋊D5
automorphism?
homologyAbelianization (H1) = C22×C41 · Schur multiplier (H2) = C2

Aliases

direct productC41×(C3⋊D3)⋊D5
unambiguous semidirect product(C3⋊D3)⋊(D5×C41)
unambiguous semidirect productD15⋊(D3×C41)

Splittings

Fitting, socle, HallC32×C5×C41 ⋊ C22
derived, HallC32×C5 ⋊ C22×C41
HallC32×C41 ⋊ C2×D5
HallC5×C41 ⋊ D32
SylowC32 ⋊ C2×D5×C41
SylowC5 ⋊ D32×C41

Subgroups

subgroupG/H
center, hypercenterC41(C3⋊D3)⋊D5
commutator, hypocenterC32×C5C22×C41
FrattiniC1G
Fitting, socleC32×C5×C41C22
LCSG ▷ C32×C5
UCSC1 ◁ C41

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

861 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC41×(C3⋊D3)⋊D25, (C3⋊D3)⋊D5×C41⋊C5, C5×C41×(C3⋊D3)⋊D5, …
maximal normal subgroup of(C3⋊D3)⋊D5×C41⋊C5, C5×C41×(C3⋊D3)⋊D5
maximal quotient ofC41×(C3⋊D3)⋊D25, C5×C41×(C3⋊D3)⋊D5, C41×D15⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 124);