Finite Group Databasebeta

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C5×D861 #22575558

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

Aliases

direct productC5×D861
unambiguous semidirect productC3⋊(C5×D287)
unambiguous semidirect productC7⋊(C5×D123)

Splittings

Fitting, socle, HallC3×C5×C7×C41 ⋊ C2
derived, HallC3×C7×C41 ⋊ C2×C5
HallC5×C7×C41 ⋊ D3
HallC3×C5×C41 ⋊ D7
HallC7×C41 ⋊ C5×D3
HallC5×C41 ⋊ D21
HallC3×C41 ⋊ C5×D7
HallC3×C5×C7 ⋊ D41
SylowC41 ⋊ C5×D21
HallC5×C7 ⋊ D123
HallC3×C7 ⋊ C5×D41
HallC3×C5 ⋊ D287
SylowC7 ⋊ C5×D123
SylowC3 ⋊ C5×D287

Subgroups

subgroupG/H
center, hypercenterC5D861
commutator, hypocenterC3×C7×C41C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2
LCSG ▷ C3×C7×C41
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D21×D41, C5×D7×D123, C5×D3×D287, …
maximal normal subgroup ofC5×D21×D41, C5×D7×D123, C5×D3×D287, …
maximal quotient ofC5×Dic861, C2×C5×D861, C5×D2583, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8610, 15);