Finite Group Databasebeta

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C5×C11⋊#10596873 #44568479

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

Aliases

direct productC5×C11⋊#10596873

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC5×C7×Dic77 ⋊ C3
HallC5×C11×#3861 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC7×Dic77 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
HallC5×#3861 ⋊ Dic11
HallC5×C72 ⋊ C3×Dic11
Hall#3861 ⋊ C5×Dic11
HallC5×C11 ⋊ #10596873
SylowC72 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×#10596873

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊#64423
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C5×C11⋊#64423
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3861C2
cosocleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C5

144 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 181);