Finite Group Databasebeta

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C5×C9×D115 #23780356

order10350
isoclinismisoclinic class of D115
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D115
unambiguous semidirect productC5⋊(C5×C9×D23)
unambiguous semidirect productC23⋊(C5×C9×D5)

Splittings

Fitting, HallC52×C9×C23 ⋊ C2
derivedC5×C23 ⋊ C2×C5×C9
HallC52×C23 ⋊ C2×C9
HallC52×C9 ⋊ D23
HallC9×C23 ⋊ C5×D5
SylowC52 ⋊ C9×D23
SylowC23 ⋊ C5×C9×D5

Subgroups

subgroupG/H
center, hypercenterC5×C9D115
commutator, hypocenterC5×C23C2×C5×C9
FrattiniC3C3×C5×D115
FittingC52×C9×C23C2
socleC3×C52×C23C2×C3
prime radicalC3×C5×D115C3
cosocleC3×C5×C23C2×C3×C5
LCSG ▷ C5×C23
UCSC1 ◁ C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2655 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×D5×D23, C9×D5×D115, C9×(C5⋊D5)⋊D23, …
maximal normal subgroup ofC5×C9×D5×D23, C9×D5×D115, C9×(C5⋊D5)⋊D23, …
maximal quotient ofC5×C9×Dic115, C2×C5×C9×D115

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 30);