Finite Group Databasebeta

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C5×C11⋊#10596885 #44568620

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

Aliases

direct productC5×C11⋊#10596885

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ Dic3
derived, HallC11×#3862 ⋊ C4×C5
HallC5×C11×#3862 ⋊ C4
HallC5×#3862 ⋊ Dic11
HallC72×C11 ⋊ C5×Dic3
HallC5×C72 ⋊ Dic33
Hall#3862 ⋊ C5×Dic11
HallC5×C11 ⋊ #10596885
SylowC72 ⋊ C5×Dic33
SylowC11 ⋊ C5×#10596885

Subgroups

subgroupG/H
center, hypercenterC5C11⋊#10596885
commutator, hypocenterC11×#3862C4×C5
FrattiniC1G
Fitting, socleC5×C72×C11Dic3
prime radicalC5×C11×#64425C2
cosocleC11×#64425C2×C5
LCSG ▷ C11×#3862
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 322);