Finite Group Databasebeta

← Prev (#49179135) Next (#49179137) →

C23×D819 #49179136

order37674
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D819
unambiguous semidirect productC7⋊(C23×D117)
unambiguous semidirect productC9⋊(C23×D91)
unambiguous semidirect productC13⋊(C23×D63)

Splittings

Fitting, HallC7×C9×C13×C23 ⋊ C2
derived, HallC7×C9×C13 ⋊ C2×C23
HallC9×C13×C23 ⋊ D7
HallC7×C13×C23 ⋊ D9
HallC7×C9×C23 ⋊ D13
HallC13×C23 ⋊ D63
HallC9×C23 ⋊ D91
HallC7×C23 ⋊ D117
HallC9×C13 ⋊ D7×C23
HallC7×C13 ⋊ D9×C23
HallC7×C9 ⋊ C23×D13
SylowC13 ⋊ C23×D63
SylowC9 ⋊ C23×D91
SylowC7 ⋊ C23×D117

Subgroups

subgroupG/H
center, hypercenterC23D819
commutator, cosocle, hypocenterC7×C9×C13C2×C23
FrattiniC3C23×D273
FittingC7×C9×C13×C23C2
socleC3×C7×C13×C23D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18837

Conjugacy classes & character table

9453 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37674, 19);