Finite Group Databasebeta

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C3×C5×D287 #22575550

order8610
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D287

Splittings

Fitting, socle, HallC3×C5×C7×C41 ⋊ C2
derived, HallC7×C41 ⋊ C2×C3×C5
HallC5×C7×C41 ⋊ C2×C3
HallC3×C7×C41 ⋊ C2×C5
HallC3×C5×C41 ⋊ D7
HallC5×C41 ⋊ C3×D7
HallC3×C41 ⋊ C5×D7
HallC3×C5×C7 ⋊ D41
SylowC41 ⋊ C3×C5×D7
HallC5×C7 ⋊ C3×D41
HallC3×C7 ⋊ C5×D41
SylowC7 ⋊ C3×C5×D41

Subgroups

subgroupG/H
center, hypercenterC3×C5D287
commutator, hypocenterC7×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2
LCSG ▷ C7×C41
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2175 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D7×D41, C3×D5×D287, C3×D35⋊D41, …
maximal normal subgroup ofC3×C5×D7×D41, C3×D5×D287, C3×D35⋊D41, …
maximal quotient ofC3×C5×Dic287, C2×C3×C5×D287, C5×C9×D287, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8610, 7);