Finite Group Databasebeta

← Prev (#44568312) Next (#44568314) →

C5×Dic1617 #44568313

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

Aliases

direct productC5×Dic1617
unambiguous semidirect productC3⋊(C5×Dic539)
unambiguous semidirect productC49⋊(C5×Dic33)

Splittings

derived, HallC3×C11×C49 ⋊ C4×C5
HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ Dic3
HallC3×C5×C49 ⋊ Dic11
HallC11×C49 ⋊ C5×Dic3
HallC5×C49 ⋊ Dic33
HallC3×C5×C11 ⋊ Dic49
HallC3×C49 ⋊ C5×Dic11
HallC5×C11 ⋊ Dic147
SylowC49 ⋊ C5×Dic33
HallC3×C11 ⋊ C5×Dic49
HallC3×C5 ⋊ Dic539
SylowC11 ⋊ C5×Dic147
SylowC3 ⋊ C5×Dic539

Subgroups

subgroupG/H
center, hypercenterC2×C5D1617
commutator, hypocenterC3×C11×C49C4×C5
FrattiniC2×C7C5×D231
FittingC2×C3×C5×C11×C49C2
socle, prime radicalC2×C3×C5×C7×C11D7
cosocleC2×C3×C11×C49C2×C5
LCSG ▷ C3×C11×C49
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 15);