Finite Group Databasebeta

← Prev (#44526605) Next (#44526607) →

C3×Dic2585 #44526606

order31020
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic2585
unambiguous semidirect productC11⋊(C3×Dic235)
unambiguous semidirect productC47⋊(C3×Dic55)

Splittings

derived, HallC5×C11×C47 ⋊ C3×C4
HallC3×C5×C11×C47 ⋊ C4
HallC3×C11×C47 ⋊ Dic5
HallC3×C5×C47 ⋊ Dic11
HallC11×C47 ⋊ C3×Dic5
HallC5×C47 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ Dic47
HallC3×C47 ⋊ Dic55
HallC5×C11 ⋊ C3×Dic47
SylowC47 ⋊ C3×Dic55
HallC3×C11 ⋊ Dic235
HallC3×C5 ⋊ Dic517
SylowC11 ⋊ C3×Dic235
SylowC5 ⋊ C3×Dic517

Subgroups

subgroupG/H
center, hypercenterC2×C3D2585
commutator, hypocenterC5×C11×C47C3×C4
FrattiniC2C3×D2585
Fitting, socle, prime radicalC2×C3×C5×C11×C47C2
cosocleC2×C5×C11×C47C2×C3
LCSG ▷ C5×C11×C47
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31020

Conjugacy classes & character table

7764 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 9);