Finite Group Databasebeta

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C3×ΓL(1,𝔽8)×C19⋊AGL(1,𝔽5) #37561267

order23940
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×C19⋊AGL(1,𝔽5)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C3×C4
derived, HallC5×C7×C19 ⋊ C32×C4
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C4
HallC7×C19⋊AGL(1,𝔽5) ⋊ C32
HallC3×C19×ΓL(1,𝔽8) ⋊ AGL(1,𝔽5)
HallC3×C5×ΓL(1,𝔽8) ⋊ Dic19
HallC7×C19 ⋊ C32×AGL(1,𝔽5)
HallC5×C19 ⋊ C3×C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C32×Dic19
SylowC19 ⋊ C3×AGL(1,𝔽5)×ΓL(1,𝔽8)
SylowC7 ⋊ C32×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×ΓL(1,𝔽8)×Dic19

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×C19⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7×C19C32×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C19C3×C4
prime radicalC3×D5×C19×ΓL(1,𝔽8)C2
cosocleC7×D5×C19C2×C32
LCSG ▷ C5×C7×C19
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1995

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 399);