Finite Group Databasebeta

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C5×C11⋊(#5997⋊C3) #44568622

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

Aliases

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

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C3×C4
derived, HallC72×C11 ⋊ C3×C4×C5
HallC5×C11⋊#5997 ⋊ C3
HallC5×C11×#3861 ⋊ C4
HallC11⋊#5997 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
HallC5×#3861 ⋊ Dic11
HallC5×C72 ⋊ C3×Dic11
Hall#3861 ⋊ C5×Dic11
HallC5×C11 ⋊ #5997⋊C3
SylowC72 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×#5997⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C11⋊(#5997⋊C3)
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalC5×C11×#64424C2
cosocleC11×C7⋊D7C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 324);