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C2×C7×D5×C13⋊C3 #19129797

order5460
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D5×C13⋊C3
unambiguous semidirect productC5⋊(C22×C7×C13⋊C3)
unambiguous semidirect product(C2×C5)⋊(C2×C7×C13⋊C3)
unambiguous semidirect product(C2×D5×C13)⋊(C3×C7)

Splittings

Fitting, socleC2×C5×C7×C13 ⋊ C2×C3
derived, HallC5×C13 ⋊ C22×C3×C7
HallC2×C7×D5×C13 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C22
HallC5×C7×C13 ⋊ C22×C3
HallC2×D5×C13 ⋊ C3×C7
HallC5×C13⋊C3 ⋊ C22×C7
HallC7×C13 ⋊ C2×C3×D5
HallC5×C7 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×C3×C7×D5
SylowC5 ⋊ C22×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7D5×C13⋊C3
commutator, hypocenterC5×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

392 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D5×ΓL(1,𝔽8)×C13⋊C3, D3×C7×D5×C13⋊C3, C2×C3×C7×D5×C13⋊C3, …
maximal normal subgroup ofC2×D5×ΓL(1,𝔽8)×C13⋊C3, C2×C3×C7×D5×C13⋊C3, C2×C5×C7×D5×C13⋊C3, …
maximal quotient ofC2×C7×D5×C13⋊C9, D3×C7×D5×C13⋊C3, C2×C3×C7×D5×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 139);