Finite Group Databasebeta

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C2×C3×C5×C7×D59 #37613428

order24780
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C7×D59
unambiguous semidirect productC59⋊(C22×C3×C5×C7)
unambiguous semidirect product(C2×C59)⋊(C2×C3×C5×C7)

Splittings

Fitting, socleC2×C3×C5×C7×C59 ⋊ C2
derived, SylowC59 ⋊ C22×C3×C5×C7
HallC3×C5×C7×C59 ⋊ C22
HallC5×C7×C59 ⋊ C22×C3
HallC3×C7×C59 ⋊ C22×C5
HallC3×C5×C59 ⋊ C22×C7
HallC7×C59 ⋊ C22×C3×C5
HallC5×C59 ⋊ C22×C3×C7
HallC3×C59 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D59
commutator, cosocle, hypocenterC59C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C59C2
LCSG ▷ C59
UCSC1 ◁ C2×C3×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12390

Conjugacy classes & character table

6510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 90);