Finite Group Databasebeta

← Prev (#37561035) Next (#37561037) →

C5×C7×C22⋊#4294 #37561036

order23940
automorphism?
homologyAbelianization (H1) = C5×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×C22⋊#4294
unambiguous semidirect productC22⋊(C5×C7×#4294)
unambiguous semidirect product(C22×C5)⋊(C7×#4294)

Splittings

derived, HallC22×C19 ⋊ C5×C7×C9
HallC22×C5×C7×C19 ⋊ C9
HallC5×C7×C19 ⋊ C22⋊C9
HallC22×C7×C19 ⋊ C5×C9
HallC22×C5×C19 ⋊ C7×C9
HallC22×C5×C7 ⋊ #4294
HallC7×C19 ⋊ C5×C22⋊C9
HallC5×C19 ⋊ C7×C22⋊C9
HallC22×C7 ⋊ C5×#4294
HallC22×C5 ⋊ C7×#4294
SylowC19 ⋊ C5×C7×C22⋊C9
SylowC22 ⋊ C5×C7×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C5×C7×C9
FrattiniC3C5×C7×C22⋊(C19⋊C3)
Fitting, socle, prime radicalC22×C3×C5×C7×C19C3
cosocleC22×C3×C19C3×C5×C7
LCSG ▷ C22×C19
UCSC1 ◁ C3×C5×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11970

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 168);