Finite Group Databasebeta

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C5×C19×Dic63 #37560883

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

Aliases

direct productC5×C19×Dic63
unambiguous semidirect productC7⋊(C5×C19×Dic9)
unambiguous semidirect productC9⋊(C5×C19×Dic7)

Splittings

derived, HallC7×C9 ⋊ C4×C5×C19
HallC5×C7×C9×C19 ⋊ C4
HallC7×C9×C19 ⋊ C4×C5
HallC5×C9×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ Dic9
HallC5×C7×C9 ⋊ C4×C19
HallC9×C19 ⋊ C5×Dic7
HallC7×C19 ⋊ C5×Dic9
HallC5×C9 ⋊ C19×Dic7
HallC5×C7 ⋊ C19×Dic9
SylowC9 ⋊ C5×C19×Dic7
SylowC7 ⋊ C5×C19×Dic9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19D63
commutator, hypocenterC7×C9C4×C5×C19
FrattiniC2×C3C5×C19×D21
FittingC2×C5×C7×C9×C19C2
socle, prime radicalC2×C3×C5×C7×C19D3
cosocleC2×C7×C9C2×C5×C19
LCSG ▷ C7×C9
UCSC1 ◁ C2×C5×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

6270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 15);