Finite Group Databasebeta

← Prev (#37560884) Next (#37560886) →

C7×C19×Dic45 #37560885

order23940
automorphism?
homologyAbelianization (H1) = C4×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19×Dic45
unambiguous semidirect productC9⋊(C7×C19×Dic5)

Splittings

derived, HallC5×C9 ⋊ C4×C7×C19
HallC5×C7×C9×C19 ⋊ C4
HallC7×C9×C19 ⋊ Dic5
HallC5×C9×C19 ⋊ C4×C7
HallC5×C7×C19 ⋊ Dic9
HallC5×C7×C9 ⋊ C4×C19
HallC9×C19 ⋊ C7×Dic5
HallC5×C19 ⋊ C7×Dic9
HallC7×C9 ⋊ C19×Dic5
HallC5×C7 ⋊ C19×Dic9
SylowC9 ⋊ C7×C19×Dic5
SylowC5 ⋊ C7×C19×Dic9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C19D45
commutator, hypocenterC5×C9C4×C7×C19
FrattiniC2×C3C7×C19×D15
FittingC2×C5×C7×C9×C19C2
socle, prime radicalC2×C3×C5×C7×C19D3
cosocleC2×C5×C9C2×C7×C19
LCSG ▷ C5×C9
UCSC1 ◁ C2×C7×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

6384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 17);