Finite Group Databasebeta

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C59×C22⋊(C43⋊C3) #44478495

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

Aliases

direct productC59×C22⋊(C43⋊C3)
unambiguous semidirect productC22⋊(C59×C43⋊C3)
unambiguous semidirect productC43⋊(A4×C59)
unambiguous semidirect product(C22×C59)⋊(C43⋊C3)
unambiguous semidirect product(C43×C59)⋊A4

Splittings

Fitting, socle, HallC22×C43×C59 ⋊ C3
derived, HallC22×C43 ⋊ C3×C59
HallC43×C59 ⋊ A4
HallC22×C59 ⋊ C43⋊C3
SylowC43 ⋊ A4×C59
SylowC22 ⋊ C59×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC59C22⋊(C43⋊C3)
commutator, cosocle, hypocenterC22×C43C3×C59
FrattiniC1G
Fitting, socleC22×C43×C59C3
LCSG ▷ C22×C43
UCSC1 ◁ C59

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10148

Conjugacy classes & character table

3540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30444, 26);