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C5×#13109896 #22551189

order8190
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#13109896

Splittings

derived, HallC7×C13 ⋊ C2×C5×C9
HallC5×#11717941 ⋊ C2
HallC5×C7×D13 ⋊ C9
Hall#11717941 ⋊ C2×C5
HallC5×C7×C13 ⋊ C2×C9
HallC7×D13 ⋊ C5×C9
HallC5×D13 ⋊ C7⋊C9
HallC5×C13 ⋊ C2×C7⋊C9
HallC5×C7 ⋊ D13⋊C9
HallD13 ⋊ C5×C7⋊C9
SylowC13 ⋊ C2×C5×C7⋊C9
SylowC7 ⋊ C5×D13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5#10587716
commutator, hypocenterC7×C13C2×C5×C9
FrattiniC3C5×#10587716
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#15692592, C5×#13109896⋊C2, C5×#15692589, …
maximal normal subgroup ofC5×#15692592, C5×#13109896⋊C2, C5×#15692589, …
maximal quotient ofC5×#15692565, C2×C5×#13109896

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 23);