Finite Group Databasebeta

← Prev (#37560901) Next (#37560903) →

C19×Dic5×C7⋊C9 #37560902

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

Aliases

direct productC19×Dic5×C7⋊C9
unambiguous semidirect product(C7×Dic5)⋊(C9×C19)

Splittings

derived, HallC5×C7 ⋊ C4×C9×C19
HallC5×C19×C7⋊C9 ⋊ C4
HallC7×C19×Dic5 ⋊ C9
HallC5×C7×C19 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C19
HallC7×Dic5 ⋊ C9×C19
HallC7×C19 ⋊ C9×Dic5
HallC5×C19 ⋊ C4×C7⋊C9
SylowC7 ⋊ C9×C19×Dic5
SylowC5 ⋊ C4×C19×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C4×C9×C19
FrattiniC2×C3D5×C19×ΓL(1,𝔽8)
Fitting, socle, prime radicalC2×C3×C5×C7×C19C2×C3
cosocleC2×C3×C5×C7C2×C3×C19
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

2280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 34);