Finite Group Databasebeta

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C2×C5×D3×C7×C13 #19129887

order5460
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D3×C7×C13
unambiguous semidirect productC3⋊(C22×C5×C7×C13)
unambiguous semidirect product(C2×C3)⋊(C2×C5×C7×C13)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2
derived, SylowC3 ⋊ C22×C5×C7×C13
HallC3×C5×C7×C13 ⋊ C22
HallC3×C7×C13 ⋊ C22×C5
HallC3×C5×C13 ⋊ C22×C7
HallC3×C5×C7 ⋊ C22×C13
HallC3×C13 ⋊ C22×C5×C7
HallC3×C7 ⋊ C22×C5×C13
HallC3×C5 ⋊ C22×C7×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C13D3
commutator, hypocenterC3C22×C5×C7×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3
UCSC1 ◁ C2×C5×C7×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C7×C13×D9, C2×C5×D3×C7×C13⋊C3, C2×C5×D3×C13×ΓL(1,𝔽8), …
maximal normal subgroup ofC2×C5×D3×C7×C13⋊C3, C2×C5×D3×C13×ΓL(1,𝔽8), C2×C5×D3×#63270, …
maximal quotient ofC2×C5×C7×C13×D9, C5×D32×C7×C13, C2×C5×C7×C13×C3⋊D3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 229);