Finite Group Databasebeta

← Prev (#44568817) Next (#44568819) →

C3×C11⋊#11758267 #44568818

order32340
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productC3×C11⋊#11758267
unambiguous semidirect productC11⋊(C3×#11758267)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ Dic5
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ C3×Dic5
HallC5×C72 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ #5997
HallC3×C72 ⋊ Dic55
HallC5×C11 ⋊ C3×#5997
SylowC72 ⋊ C3×Dic55
HallC3×C11 ⋊ #11758267
HallC3×C5 ⋊ C11⋊#5997
SylowC11 ⋊ C3×#11758267
SylowC5 ⋊ C3×C11⋊#5997

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#11758267
commutator, hypocenterC5×C72×C11C3×C4
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C5×C11×C7⋊D7C2
cosocleC5×C11×C7⋊D7C2×C3
LCSG ▷ C5×C72×C11
UCSC1 ◁ C3

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2154 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 520);