Finite Group Databasebeta

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C4×C5×C19×C7⋊C9 #37560871

order23940
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C19 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C19×C7⋊C9
unambiguous semidirect product(C4×C7)⋊(C5×C9×C19)
unambiguous semidirect product(C4×C5×C7)⋊(C9×C19)

Splittings

derived, SylowC7 ⋊ C4×C5×C9×C19
HallC4×C5×C7×C19 ⋊ C9
HallC5×C7×C19 ⋊ C4×C9
HallC4×C7×C19 ⋊ C5×C9
HallC4×C5×C7 ⋊ C9×C19
HallC7×C19 ⋊ C4×C5×C9
HallC5×C7 ⋊ C4×C9×C19
HallC4×C7 ⋊ C5×C9×C19

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C19ΓL(1,𝔽8)
commutator, hypocenterC7C4×C5×C9×C19
FrattiniC2×C3C2×C5×C19×ΓL(1,𝔽8)
FittingC3×C4×C5×C7×C19C3
socle, prime radicalC2×C3×C5×C7×C19C2×C3
cosocleC2×C3×C7C2×C3×C5×C19
LCSG ▷ C7
UCSC1 ◁ C3×C4×C5×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

5700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 3);