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C3×(C241⋊C3)⋊C5 #24925724

order10845
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C241⋊C3)⋊C5
unambiguous semidirect product(C241⋊C3)⋊(C3×C5)
unambiguous semidirect product(C241⋊C5)⋊C32
unambiguous semidirect product(C3×C241⋊C3)⋊C5
unambiguous semidirect product(C3×C241⋊C5)⋊C3

Splittings

Fitting, socleC3×C241 ⋊ C3×C5
derived, SylowC241 ⋊ C32×C5
HallC3×C241⋊C3 ⋊ C5
HallC241⋊C5 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3(C241⋊C3)⋊C5
commutator, cosocle, hypocenterC241C32×C5
FrattiniC1G
Fitting, socleC3×C241C3×C5
LCSG ▷ C241
UCSC1 ◁ C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(D241⋊C3)⋊C5, C3⋊((D241⋊C3)⋊C5), D3×(C241⋊C3)⋊C5, …
maximal normal subgroup ofC3×(D241⋊C3)⋊C5, C3⋊((D241⋊C3)⋊C5), D3×(C241⋊C3)⋊C5, …
maximal quotient ofC2×C3×(C241⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10845, 6);