Finite Group Databasebeta

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C3×D1505 #22583281

order9030
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D1505
unambiguous semidirect productC5⋊(C3×D301)

Splittings

Fitting, socle, HallC3×C5×C7×C43 ⋊ C2
derived, HallC5×C7×C43 ⋊ C2×C3
HallC3×C7×C43 ⋊ D5
HallC3×C5×C43 ⋊ D7
HallC7×C43 ⋊ C3×D5
HallC5×C43 ⋊ C3×D7
HallC3×C43 ⋊ D35
HallC3×C5×C7 ⋊ D43
SylowC43 ⋊ C3×D35
HallC5×C7 ⋊ C3×D43
HallC3×C7 ⋊ D215
HallC3×C5 ⋊ D301
SylowC7 ⋊ C3×D215
SylowC5 ⋊ C3×D301

Subgroups

subgroupG/H
center, hypercenterC3D1505
commutator, hypocenterC5×C7×C43C2×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C43C2
LCSG ▷ C5×C7×C43
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2262 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D35×D43, C3×D7×D215, C3×D5×D301, …
maximal normal subgroup ofC3×D35×D43, C3×D7×D215, C3×D5×D301, …
maximal quotient ofC3×Dic1505, C2×C3×D1505, C9×D1505, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 14);