Finite Group Databasebeta

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C4×C5×#11925881 #37563707

order24180
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#11925881

Splittings

Fitting, HallC4×C5×C13×C31 ⋊ C3
derived, HallC13×C31 ⋊ C3×C4×C5
HallC5×C13×C31 ⋊ C3×C4
HallC4×C13×C31 ⋊ C3×C5
HallC4×C5×C31 ⋊ C13⋊C3
HallC4×C5×C13 ⋊ C31⋊C3
HallC5×C31 ⋊ C4×C13⋊C3
HallC4×C31 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C4×C31⋊C3
HallC4×C13 ⋊ C5×C31⋊C3
SylowC31 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C4×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C5#11925881
commutator, hypocenterC13×C31C3×C4×C5
FrattiniC2C2×C5×#11925881
FittingC4×C5×C13×C31C3
socleC2×C5×C13×C31C2×C3
prime radicalC2×C5×#11925881C2
cosocleC2×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C4×C5

48 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, 6);