Finite Group Databasebeta

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C3×D1435 #22575554

order8610
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D1435
unambiguous semidirect productC5⋊(C3×D287)
unambiguous semidirect productC41⋊(C3×D35)

Splittings

Fitting, socle, HallC3×C5×C7×C41 ⋊ C2
derived, HallC5×C7×C41 ⋊ C2×C3
HallC3×C7×C41 ⋊ D5
HallC3×C5×C41 ⋊ D7
HallC7×C41 ⋊ C3×D5
HallC5×C41 ⋊ C3×D7
HallC3×C41 ⋊ D35
HallC3×C5×C7 ⋊ D41
SylowC41 ⋊ C3×D35
HallC5×C7 ⋊ C3×D41
HallC3×C7 ⋊ D205
HallC3×C5 ⋊ D287
SylowC7 ⋊ C3×D205
SylowC5 ⋊ C3×D287

Subgroups

subgroupG/H
center, hypercenterC3D1435
commutator, hypocenterC5×C7×C41C2×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2
LCSG ▷ C5×C7×C41
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2157 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D35×D41, C3×D7×D205, C3×D5×D287, …
maximal normal subgroup ofC3×D35×D41, C3×D7×D205, C3×D5×D287, …
maximal quotient ofC3×Dic1435, C2×C3×D1435, C9×D1435, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8610, 11);