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C2×C5×#10587717 #19129792

order5460
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#10587717

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C5
HallC2×C5×C7×D13 ⋊ C3
HallC5×#63271 ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC2×C7×D13 ⋊ C3×C5
Hall#63271 ⋊ C22×C5
HallC2×C5×D13 ⋊ ΓL(1,𝔽8)
HallC5×C13 ⋊ C22×ΓL(1,𝔽8)
HallC2×D13 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×D13⋊C3
SylowC13 ⋊ C22×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#10587717
commutator, hypocenterC7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×ΓL(1,𝔽8)×D13⋊C3, C5×D3×#10587717, C2×C3×C5×#10587717, …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)×D13⋊C3, C2×C3×C5×#10587717, C2×C25×#10587717, …
maximal quotient ofC2×C5×#13109897, C5×D3×#10587717, C2×C3×C5×#10587717, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 134);