Finite Group Databasebeta

← Prev (#49185808) Next (#49185810) →

C5×D41×C31⋊C3 #49185809

order38130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D41×C31⋊C3
unambiguous semidirect product(C5×C31×D41)⋊C3

Splittings

Fitting, socle, HallC5×C31×C41 ⋊ C2×C3
derived, HallC31×C41 ⋊ C2×C3×C5
HallC5×C41×C31⋊C3 ⋊ C2
HallC5×C31×D41 ⋊ C3
HallC41×C31⋊C3 ⋊ C2×C5
HallC31×D41 ⋊ C3×C5
HallC5×C41 ⋊ C2×C31⋊C3
HallC5×C31 ⋊ C3×D41
SylowC41 ⋊ C2×C5×C31⋊C3
SylowC31 ⋊ C3×C5×D41

Subgroups

subgroupG/H
center, hypercenterC5D41×C31⋊C3
commutator, cosocle, hypocenterC31×C41C2×C3×C5
FrattiniC1G
Fitting, socleC5×C31×C41C2×C3
LCSG ▷ C31×C41
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6355

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38130, 72);