Finite Group Databasebeta

← Prev (#37563734) Next (#37563736) →

C5×C13⋊C3×Dic31 #37563735

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

Aliases

direct productC5×C13⋊C3×Dic31

Splittings

derived, HallC13×C31 ⋊ C3×C4×C5
HallC5×C13×Dic31 ⋊ C3
HallC5×C31×C13⋊C3 ⋊ C4
HallC5×C13×C31 ⋊ C3×C4
HallC13×Dic31 ⋊ C3×C5
HallC31×C13⋊C3 ⋊ C4×C5
HallC5×C31 ⋊ C4×C13⋊C3
HallC5×C13 ⋊ C3×Dic31
SylowC31 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C5×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊C3×D31
commutator, hypocenterC13×C31C3×C4×C5
FrattiniC2C5×C13⋊C3×D31
Fitting, socleC2×C5×C13×C31C2×C3
prime radicalC2×C5×C31×C13⋊C3C2
cosocleC2×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8060

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 34);