Finite Group Databasebeta

← Prev (#37563997) Next (#37563999) →

C22×C5×#11925882 #37563998

order24180
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×#11925882

Splittings

Fitting, socle, HallC22×C5×C13×C31 ⋊ C3
derived, HallC13×C31 ⋊ C22×C3×C5
HallC5×C13×C31 ⋊ C22×C3
HallC22×C13×C31 ⋊ C3×C5
HallC22×C5×C31 ⋊ C13⋊C3
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 ⋊ C22×C5×C13⋊C3
SylowC13 ⋊ C22×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C5#11925882
commutator, cosocle, hypocenterC13×C31C22×C3×C5
FrattiniC1G
Fitting, socleC22×C5×C13×C31C3
LCSG ▷ C13×C31
UCSC1 ◁ C22×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8060

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 297);