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C7×D15⋊D59 #37613412

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

Aliases

direct productC7×D15⋊D59
unambiguous semidirect productD15⋊(C7×D59)
unambiguous semidirect productD177⋊(C7×D5)
unambiguous semidirect productD295⋊(D3×C7)

Splittings

Fitting, socle, HallC3×C5×C7×C59 ⋊ C22
derived, HallC3×C5×C59 ⋊ C22×C7
HallC5×C7×C59 ⋊ C2×D3
HallC3×C7×C59 ⋊ C2×D5
HallC7×C59 ⋊ D3×D5
HallC5×C59 ⋊ C2×D3×C7
HallC3×C59 ⋊ C2×C7×D5
HallC3×C5×C7 ⋊ C2×D59
SylowC59 ⋊ D3×C7×D5
HallC5×C7 ⋊ D3×D59
HallC3×C7 ⋊ D5×D59
HallC3×C5 ⋊ C2×C7×D59
SylowC5 ⋊ D3×C7×D59
SylowC3 ⋊ C7×D5×D59

Subgroups

subgroupG/H
center, hypercenterC7D15⋊D59
commutator, cosocle, hypocenterC3×C5×C59C22×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C59C22
LCSG ▷ C3×C5×C59
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6195

Conjugacy classes & character table

1911 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 74);