Finite Group Databasebeta

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D3×C7×D5×C59 #37613409

order24780
automorphism?
homologyAbelianization (H1) = C22×C7×C59 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D5×C59
unambiguous semidirect product(C5×D3)⋊(C2×C7×C59)
unambiguous semidirect product(C3×D5)⋊(C2×C7×C59)
unambiguous semidirect productD15⋊(C2×C7×C59)

Splittings

Fitting, socle, HallC3×C5×C7×C59 ⋊ C22
derived, HallC3×C5 ⋊ C22×C7×C59
HallC5×C7×C59 ⋊ C2×D3
HallC3×C7×C59 ⋊ C2×D5
HallC3×C5×C59 ⋊ C22×C7
HallC5×C59 ⋊ C2×D3×C7
HallC3×C59 ⋊ C2×C7×D5
HallC3×C5×C7 ⋊ C22×C59
HallC5×C7 ⋊ C2×D3×C59
HallC3×C7 ⋊ C2×D5×C59
SylowC5 ⋊ C2×D3×C7×C59
SylowC3 ⋊ C2×C7×D5×C59

Subgroups

subgroupG/H
center, hypercenterC7×C59D3×D5
commutator, cosocle, hypocenterC3×C5C22×C7×C59
FrattiniC1G
Fitting, socleC3×C5×C7×C59C22
LCSG ▷ C3×C5
UCSC1 ◁ C7×C59

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6195

Conjugacy classes & character table

4956 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 71);