Finite Group Databasebeta

← Prev (#44526607) Next (#44526609) →

C5×C11×Dic141 #44526608

order31020
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic141
unambiguous semidirect productC3⋊(C5×C11×Dic47)
unambiguous semidirect productC47⋊(C5×C11×Dic3)

Splittings

derived, HallC3×C47 ⋊ C4×C5×C11
HallC3×C5×C11×C47 ⋊ C4
HallC5×C11×C47 ⋊ Dic3
HallC3×C11×C47 ⋊ C4×C5
HallC3×C5×C47 ⋊ C4×C11
HallC11×C47 ⋊ C5×Dic3
HallC5×C47 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ Dic47
SylowC47 ⋊ C5×C11×Dic3
HallC3×C11 ⋊ C5×Dic47
HallC3×C5 ⋊ C11×Dic47
SylowC3 ⋊ C5×C11×Dic47

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D141
commutator, hypocenterC3×C47C4×C5×C11
FrattiniC2C5×C11×D141
Fitting, socle, prime radicalC2×C3×C5×C11×C47C2
cosocleC2×C3×C47C2×C5×C11
LCSG ▷ C3×C47
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31020

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 11);