Finite Group Databasebeta

← Prev (#44568620) Next (#44568622) →

C5×C11×#5997⋊C3 #44568621

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#5997⋊C3
unambiguous semidirect product#5997⋊(C3×C5×C11)
unambiguous semidirect product(C5×#5997)⋊(C3×C11)
unambiguous semidirect product(C5×C11×#5997)⋊C3

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C3×C4
derived, SylowC72 ⋊ C3×C4×C5×C11
HallC5×C11×#5997 ⋊ C3
HallC5×C11×#3861 ⋊ C4
HallC11×#5997 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
HallC5×#5997 ⋊ C3×C11
HallC5×#3861 ⋊ C4×C11
HallC72×C11 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×C4×C11
Hall#5997 ⋊ C3×C5×C11
Hall#3861 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11#5997⋊C3
commutator, hypocenterC72C3×C4×C5×C11
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalC5×C11×#64424C2
cosocleC7⋊D7C2×C3×C5×C11
LCSG ▷ C72
UCSC1 ◁ C5×C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 323);