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C19×C31×AGL(1,𝔽7) #37613153

order24738
automorphism?
homologyAbelianization (H1) = C2×C3×C19×C31 · Schur multiplier (H2) = C1

Aliases

direct productC19×C31×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C19×C31)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C19×C31)

Splittings

Fitting, socle, HallC7×C19×C31 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C19×C31
HallC19×ΓL(1,𝔽8)×C31 ⋊ C2
HallD7×C19×C31 ⋊ C3
HallΓL(1,𝔽8)×C31 ⋊ C2×C19
HallD7×C31 ⋊ C3×C19
HallC19×ΓL(1,𝔽8) ⋊ C2×C31
HallD7×C19 ⋊ C3×C31
HallC7×C31 ⋊ C2×C3×C19
HallC7×C19 ⋊ C2×C3×C31
HallΓL(1,𝔽8) ⋊ C2×C19×C31
HallD7 ⋊ C3×C19×C31

Subgroups

subgroupG/H
center, hypercenterC19×C31AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C3×C19×C31
FrattiniC1G
Fitting, socleC7×C19×C31C2×C3
LCSG ▷ C7
UCSC1 ◁ C19×C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4123

Conjugacy classes & character table

4123 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24738, 73);