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C7×(C19⋊C3)⋊D31 #37613137

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

Aliases

direct productC7×(C19⋊C3)⋊D31
unambiguous semidirect product(C19⋊C3)⋊(C7×D31)

Splittings

Fitting, socle, HallC7×C19×C31 ⋊ C2×C3
derived, HallC19×C31 ⋊ C2×C3×C7
HallC7×C31×C19⋊C3 ⋊ C2
HallC7×D589 ⋊ C3
HallC31×C19⋊C3 ⋊ C2×C7
HallD589 ⋊ C3×C7
HallC7×C19⋊C3 ⋊ D31
HallC7×C31 ⋊ D19⋊C3
HallC7×C19 ⋊ C3×D31
HallC19⋊C3 ⋊ C7×D31
SylowC31 ⋊ C7×D19⋊C3
SylowC19 ⋊ C3×C7×D31

Subgroups

subgroupG/H
center, hypercenterC7(C19⋊C3)⋊D31
commutator, cosocle, hypocenterC19×C31C2×C3×C7
FrattiniC1G
Fitting, socleC7×C19×C31C2×C3
LCSG ▷ C19×C31
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4123

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24738, 57);