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C2×C5×D3×C7×C59 #37613435

order24780
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C59 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D3×C7×C59
unambiguous semidirect productC3⋊(C22×C5×C7×C59)
unambiguous semidirect product(C2×C3)⋊(C2×C5×C7×C59)

Splittings

Fitting, socleC2×C3×C5×C7×C59 ⋊ C2
derived, SylowC3 ⋊ C22×C5×C7×C59
HallC3×C5×C7×C59 ⋊ C22
HallC3×C7×C59 ⋊ C22×C5
HallC3×C5×C59 ⋊ C22×C7
HallC3×C59 ⋊ C22×C5×C7
HallC3×C5×C7 ⋊ C22×C59
HallC3×C7 ⋊ C22×C5×C59
HallC3×C5 ⋊ C22×C7×C59

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C59D3
commutator, cosocle, hypocenterC3C22×C5×C7×C59
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C59C2
LCSG ▷ C3
UCSC1 ◁ C2×C5×C7×C59

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12390

Conjugacy classes & character table

12390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 97);