Finite Group Databasebeta

← Prev (#37613175) Next (#37613177) →

C31×(C19⋊C3)⋊D7 #37613176

order24738
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×(C19⋊C3)⋊D7
unambiguous semidirect product(C19⋊C3)⋊(D7×C31)

Splittings

Fitting, socle, HallC7×C19×C31 ⋊ C2×C3
derived, HallC7×C19 ⋊ C2×C3×C31
HallC7×C31×C19⋊C3 ⋊ C2
HallC31×D133 ⋊ C3
HallC31×C19⋊C3 ⋊ D7
HallC19×C31 ⋊ C3×D7
HallC7×C19⋊C3 ⋊ C2×C31
HallD133 ⋊ C3×C31
HallC7×C31 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D7×C31
SylowC19 ⋊ C3×D7×C31
SylowC7 ⋊ C31×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC31(C19⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C19C2×C3×C31
FrattiniC1G
Fitting, socleC7×C19×C31C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4123

Conjugacy classes & character table

1116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24738, 96);