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C5×#15693299 #30658741

order16590
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#15693299

Splittings

Fitting, socle, HallC5×C7×C79 ⋊ C2×C3
derived, HallC7×C79 ⋊ C2×C3×C5
HallC5×#13110306 ⋊ C2
HallC5×C7×D79 ⋊ C3
Hall#13110306 ⋊ C2×C5
HallC7×D79 ⋊ C3×C5
HallC5×D79 ⋊ ΓL(1,𝔽8)
HallC5×C79 ⋊ C2×ΓL(1,𝔽8)
HallD79 ⋊ C5×ΓL(1,𝔽8)
SylowC79 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ D79⋊C3
SylowC7 ⋊ C5×D79⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#15693299
commutator, cosocle, hypocenterC7×C79C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C79C2×C3
LCSG ▷ C7×C79
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2765

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#15693299⋊C2, #15693299⋊D5, D5×#15693299, …
maximal normal subgroup ofC5×#15693299⋊C2, #15693299⋊D5, D5×#15693299, …
maximal quotient ofC5×#20268895, C2×C5×#15693299

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16590, 24);