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C5×D903 #22583285

order9030
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D903
unambiguous semidirect productC3⋊(C5×D301)
unambiguous semidirect productC7⋊(C5×D129)
unambiguous semidirect productC43⋊(C5×D21)

Splittings

Fitting, socle, HallC3×C5×C7×C43 ⋊ C2
derived, HallC3×C7×C43 ⋊ C2×C5
HallC5×C7×C43 ⋊ D3
HallC3×C5×C43 ⋊ D7
HallC7×C43 ⋊ C5×D3
HallC5×C43 ⋊ D21
HallC3×C43 ⋊ C5×D7
HallC3×C5×C7 ⋊ D43
SylowC43 ⋊ C5×D21
HallC5×C7 ⋊ D129
HallC3×C7 ⋊ C5×D43
HallC3×C5 ⋊ D301
SylowC7 ⋊ C5×D129
SylowC3 ⋊ C5×D301

Subgroups

subgroupG/H
center, hypercenterC5D903
commutator, hypocenterC3×C7×C43C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C43C2
LCSG ▷ C3×C7×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2265 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D21×D43, C5×D7×D129, C5×D3×D301, …
maximal normal subgroup ofC5×D21×D43, C5×D7×D129, C5×D3×D301, …
maximal quotient ofC5×Dic903, C2×C5×D903, C5×D2709, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 18);