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C5×C9×D205 #32914379

order18450
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D205
unambiguous semidirect productC5⋊(C5×C9×D41)

Splittings

Fitting, HallC52×C9×C41 ⋊ C2
derivedC5×C41 ⋊ C2×C5×C9
HallC52×C41 ⋊ C2×C9
HallC9×C41 ⋊ C5×D5
HallC52×C9 ⋊ D41
SylowC41 ⋊ C5×C9×D5
SylowC52 ⋊ C9×D41

Subgroups

subgroupG/H
center, hypercenterC5×C9D205
commutator, hypocenterC5×C41C2×C5×C9
FrattiniC3C3×C5×D205
FittingC52×C9×C41C2
socleC3×C52×C41C2×C3
prime radicalC3×C5×D205C3
cosocleC3×C5×C41C2×C3×C5
LCSG ▷ C5×C41
UCSC1 ◁ C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3690

Conjugacy classes & character table

4680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×#11717961, C5×C9×#11717962, C5×C9×D5×D41, …
maximal normal subgroup ofC5×C9×#11717961, C5×C9×#11717962, C5×C9×D5×D41, …
maximal quotient ofC5×C9×Dic205, C2×C5×C9×D205

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18450, 48);