Finite Group Databasebeta

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C2×C5×C7×D39 #19129888

order5460
isoclinismisoclinic class of D39
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D39
unambiguous semidirect product(C2×C3)⋊(C5×C7×D13)
unambiguous semidirect product(C2×C13)⋊(C5×D3×C7)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2
derived, HallC3×C13 ⋊ C22×C5×C7
HallC3×C5×C7×C13 ⋊ C22
HallC5×C7×C13 ⋊ C2×D3
HallC3×C7×C13 ⋊ C22×C5
HallC3×C5×C13 ⋊ C22×C7
HallC3×C5×C7 ⋊ C2×D13
HallC7×C13 ⋊ C2×C5×D3
HallC5×C13 ⋊ C2×D3×C7
HallC3×C7 ⋊ C2×C5×D13
HallC3×C5 ⋊ C2×C7×D13
SylowC13 ⋊ C2×C5×D3×C7
SylowC3 ⋊ C2×C5×C7×D13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D39
commutator, hypocenterC3×C13C22×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3×C13
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C7×D117, C2×C5×C7×C3⋊(D13⋊C3), C2×C5×C3⋊#10587716, …
maximal normal subgroup ofC2×C5×C7×C3⋊(D13⋊C3), C2×C5×C3⋊#10587716, C2×C5×C3⋊#10587717, …
maximal quotient ofC2×C5×C7×D117, C5×D3×C7×D39, C2×C5×C7×C3⋊D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 230);