Finite Group Databasebeta

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C2×C59×D43⋊C3 #44478484

order30444
automorphism?
homologyAbelianization (H1) = C22×C3×C59 · Schur multiplier (H2) = C2

Aliases

direct productC2×C59×D43⋊C3
unambiguous semidirect productD43⋊(C2×C3×C59)
unambiguous semidirect product(C43⋊C3)⋊(C22×C59)
unambiguous semidirect product(C2×D43)⋊(C3×C59)
unambiguous semidirect product(C2×C43⋊C3)⋊(C2×C59)
unambiguous semidirect product(C2×C59×D43)⋊C3

Splittings

Fitting, socleC2×C43×C59 ⋊ C2×C3
derived, SylowC43 ⋊ C22×C3×C59
HallC2×C59×D43 ⋊ C3
HallC59×C43⋊C3 ⋊ C22
HallC43×C59 ⋊ C22×C3
HallC2×D43 ⋊ C3×C59
HallC43⋊C3 ⋊ C22×C59

Subgroups

subgroupG/H
center, hypercenterC2×C59D43⋊C3
commutator, cosocle, hypocenterC43C22×C3×C59
FrattiniC1G
Fitting, socleC2×C43×C59C2×C3
LCSG ▷ C43
UCSC1 ◁ C2×C59

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5074

Conjugacy classes & character table

1534 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30444, 15);