Finite Group Databasebeta

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C7×C31×D19⋊C3 #37613124

order24738
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productC7×C31×D19⋊C3
unambiguous semidirect productD19⋊(C3×C7×C31)
unambiguous semidirect product(C19⋊C3)⋊(C2×C7×C31)

Splittings

Fitting, socle, HallC7×C19×C31 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C7×C31
HallC7×C31×C19⋊C3 ⋊ C2
HallC7×C31×D19 ⋊ C3
HallC31×C19⋊C3 ⋊ C2×C7
HallC31×D19 ⋊ C3×C7
HallC19×C31 ⋊ C2×C3×C7
HallC7×C19⋊C3 ⋊ C2×C31
HallC7×D19 ⋊ C3×C31
HallC7×C19 ⋊ C2×C3×C31
HallC19⋊C3 ⋊ C2×C7×C31
HallD19 ⋊ C3×C7×C31

Subgroups

subgroupG/H
center, hypercenterC7×C31D19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C7×C31
FrattiniC1G
Fitting, socleC7×C19×C31C2×C3
LCSG ▷ C19
UCSC1 ◁ C7×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4123

Conjugacy classes & character table

1953 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24738, 44);