Finite Group Databasebeta

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C5×C11⋊#10596868 #44568489

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

Aliases

direct productC5×C11⋊#10596868

Splittings

derived, HallC11×#3862 ⋊ C4×C5
HallC5×C11×#3862 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC5×#3862 ⋊ Dic11
HallC72×C11 ⋊ C5×Dic3
HallC5×C72 ⋊ Dic33
Hall#3862 ⋊ C5×Dic11
HallC5×C11 ⋊ #10596868
SylowC72 ⋊ C5×Dic33
SylowC11 ⋊ C5×#10596868

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊#64418
commutator, hypocenterC11×#3862C4×C5
FrattiniC2C5×C11⋊#64418
Fitting, socleC2×C5×C72×C11D3
prime radicalC2×C5×C11×#3862C2
cosocleC2×C11×#3862C2×C5
LCSG ▷ C11×#3862
UCSC1 ◁ C2×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 191);