Finite Group Databasebeta

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C5×D651 #20266706

order6510
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D651
unambiguous semidirect productC3⋊(C5×D217)
unambiguous semidirect productC7⋊(C5×D93)

Splittings

Fitting, socle, HallC3×C5×C7×C31 ⋊ C2
derived, HallC3×C7×C31 ⋊ C2×C5
HallC5×C7×C31 ⋊ D3
HallC3×C5×C31 ⋊ D7
HallC7×C31 ⋊ C5×D3
HallC5×C31 ⋊ D21
HallC3×C5×C7 ⋊ D31
HallC3×C31 ⋊ C5×D7
HallC5×C7 ⋊ D93
SylowC31 ⋊ C5×D21
HallC3×C7 ⋊ C5×D31
HallC3×C5 ⋊ D217
SylowC7 ⋊ C5×D93
SylowC3 ⋊ C5×D217

Subgroups

subgroupG/H
center, hypercenterC5D651
commutator, hypocenterC3×C7×C31C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C31C2
LCSG ▷ C3×C7×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1635 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D21×D31, C5×D7×D93, C5×D3×D217, …
maximal normal subgroup ofC5×D21×D31, C5×D7×D93, C5×D3×D217, …
maximal quotient ofC5×Dic651, C2×C5×D651, C5×D1953, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6510, 21);