Finite Group Databasebeta

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C3×D1085 #20266702

order6510
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D1085
unambiguous semidirect productC5⋊(C3×D217)

Splittings

Fitting, socle, HallC3×C5×C7×C31 ⋊ C2
derived, HallC5×C7×C31 ⋊ C2×C3
HallC3×C7×C31 ⋊ D5
HallC3×C5×C31 ⋊ D7
HallC7×C31 ⋊ C3×D5
HallC5×C31 ⋊ C3×D7
HallC3×C5×C7 ⋊ D31
HallC3×C31 ⋊ D35
HallC5×C7 ⋊ C3×D31
SylowC31 ⋊ C3×D35
HallC3×C7 ⋊ D155
HallC3×C5 ⋊ D217
SylowC7 ⋊ C3×D155
SylowC5 ⋊ C3×D217

Subgroups

subgroupG/H
center, hypercenterC3D1085
commutator, hypocenterC5×C7×C31C2×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2
LCSG ▷ C5×C7×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1632 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D31×D35, C3×D7×D155, C3×D5×D217, …
maximal normal subgroup ofC3×D31×D35, C3×D7×D155, C3×D5×D217, …
maximal quotient ofC3×Dic1085, C2×C3×D1085, C9×D1085, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6510, 17);