Finite Group Databasebeta

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C19×Dic315 #37560887

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

Aliases

direct productC19×Dic315
unambiguous semidirect productC7⋊(C19×Dic45)
unambiguous semidirect productC9⋊(C19×Dic35)

Splittings

derived, HallC5×C7×C9 ⋊ C4×C19
HallC5×C7×C9×C19 ⋊ C4
HallC7×C9×C19 ⋊ Dic5
HallC5×C9×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ Dic9
HallC9×C19 ⋊ Dic35
HallC7×C19 ⋊ Dic45
HallC5×C19 ⋊ Dic63
HallC7×C9 ⋊ C19×Dic5
HallC5×C9 ⋊ C19×Dic7
HallC5×C7 ⋊ C19×Dic9
SylowC9 ⋊ C19×Dic35
SylowC7 ⋊ C19×Dic45
SylowC5 ⋊ C19×Dic63

Subgroups

subgroupG/H
center, hypercenterC2×C19D315
commutator, hypocenterC5×C7×C9C4×C19
FrattiniC2×C3C19×D105
FittingC2×C5×C7×C9×C19C2
socle, prime radicalC2×C3×C5×C7×C19D3
cosocleC2×C5×C7×C9C2×C19
LCSG ▷ C5×C7×C9
UCSC1 ◁ C2×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

6042 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 19);