Finite Group Databasebeta

← Prev (#36339030) Next (#36339032) →

C5×C23×D31⋊C3 #36339031

order21390
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×D31⋊C3
unambiguous semidirect product(C5×D31)⋊(C3×C23)
unambiguous semidirect product(C5×C23×D31)⋊C3

Splittings

Fitting, socle, HallC5×C23×C31 ⋊ C2×C3
derived, SylowC31 ⋊ C2×C3×C5×C23
HallC5×C23×C31⋊C3 ⋊ C2
HallC5×C23×D31 ⋊ C3
HallC23×C31⋊C3 ⋊ C2×C5
HallC23×D31 ⋊ C3×C5
HallC23×C31 ⋊ C2×C3×C5
HallC5×C31⋊C3 ⋊ C2×C23
HallC5×D31 ⋊ C3×C23
HallC5×C31 ⋊ C2×C3×C23
HallC31⋊C3 ⋊ C2×C5×C23
HallD31 ⋊ C3×C5×C23

Subgroups

subgroupG/H
center, hypercenterC5×C23D31⋊C3
commutator, cosocle, hypocenterC31C2×C3×C5×C23
FrattiniC1G
Fitting, socleC5×C23×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C5×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3565

Conjugacy classes & character table

1265 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21390, 27);