Finite Group Databasebeta

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C3×(C11⋊C5)⋊#5997 #44568584

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×(C11⋊C5)⋊#5997
unambiguous semidirect product(C11⋊C5)⋊(C3×#5997)
unambiguous semidirect product(C3×C11⋊#5997)⋊C5

Splittings

Fitting, socle, HallC3×C72×C11 ⋊ C4×C5
derived, HallC72×C11 ⋊ C3×C4×C5
HallC3×C72×C11⋊C5 ⋊ C4
HallC3×C11⋊#5997 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC11⋊#5997 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ #5997
HallC3×C72 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×#5997
SylowC72 ⋊ C3×Dic11⋊C5
HallC3×C11 ⋊ C5×#5997
SylowC11 ⋊ C3×C5×#5997

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊#5997
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC1G
Fitting, socleC3×C72×C11C4×C5
prime radicalC3×C11⋊C5×C7⋊D7C2
cosocleC11×C7⋊D7C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C3

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 286);