Finite Group Databasebeta

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C5×C22⋊#11925881 #37563993

order24180
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#11925881
unambiguous semidirect productC22⋊(C5×#11925881)
unambiguous semidirect product(C22×C5)⋊#11925881

Splittings

Fitting, socle, HallC22×C5×C13×C31 ⋊ C3
derived, HallC22×C13×C31 ⋊ C3×C5
HallC5×C13×C31 ⋊ A4
HallC22×C5×C31 ⋊ C13⋊C3
HallC13×C31 ⋊ C5×A4
HallC22×C5×C13 ⋊ C31⋊C3
HallC5×C31 ⋊ C22⋊(C13⋊C3)
HallC22×C31 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C22⋊(C31⋊C3)
HallC22×C13 ⋊ C5×C31⋊C3
SylowC31 ⋊ C5×C22⋊(C13⋊C3)
HallC22×C5 ⋊ #11925881
SylowC13 ⋊ C5×C22⋊(C31⋊C3)
SylowC22 ⋊ C5×#11925881

Subgroups

subgroupG/H
center, hypercenterC5C22⋊#11925881
commutator, cosocle, hypocenterC22×C13×C31C3×C5
FrattiniC1G
Fitting, socleC22×C5×C13×C31C3
LCSG ▷ C22×C13×C31
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8060

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 292);