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C2×C5×C13⋊C3×C59 #37527646

order23010
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C59 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C13⋊C3×C59
unambiguous semidirect product(C2×C13)⋊(C3×C5×C59)
unambiguous semidirect product(C2×C5×C13)⋊(C3×C59)
unambiguous semidirect product(C2×C13×C59)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C13×C59)⋊C3

Splittings

Fitting, socle, HallC2×C5×C13×C59 ⋊ C3
derived, SylowC13 ⋊ C2×C3×C5×C59
HallC5×C13×C59 ⋊ C2×C3
HallC2×C13×C59 ⋊ C3×C5
HallC13×C59 ⋊ C2×C3×C5
HallC2×C5×C13 ⋊ C3×C59
HallC5×C13 ⋊ C2×C3×C59
HallC2×C13 ⋊ C3×C5×C59

Subgroups

subgroupG/H
center, hypercenterC2×C5×C59C13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C59
FrattiniC1G
Fitting, socleC2×C5×C13×C59C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7670

Conjugacy classes & character table

4130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23010, 2);