Finite Group Databasebeta

← Prev (#44568311) Next (#44568313) →

C5×C11×Dic147 #44568312

order32340
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic147
unambiguous semidirect productC3⋊(C5×C11×Dic49)
unambiguous semidirect productC49⋊(C5×C11×Dic3)

Splittings

derived, HallC3×C49 ⋊ C4×C5×C11
HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ Dic3
HallC3×C11×C49 ⋊ C4×C5
HallC3×C5×C49 ⋊ C4×C11
HallC11×C49 ⋊ C5×Dic3
HallC5×C49 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ Dic49
SylowC49 ⋊ C5×C11×Dic3
HallC3×C11 ⋊ C5×Dic49
HallC3×C5 ⋊ C11×Dic49
SylowC3 ⋊ C5×C11×Dic49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D147
commutator, hypocenterC3×C49C4×C5×C11
FrattiniC2×C7C5×C11×D21
FittingC2×C3×C5×C11×C49C2
socle, prime radicalC2×C3×C5×C7×C11D7
cosocleC2×C3×C49C2×C5×C11
LCSG ▷ C3×C49
UCSC1 ◁ C2×C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 14);