Finite Group Databasebeta

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C11⋊C5×#10596873 #44568446

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

Aliases

direct productC11⋊C5×#10596873
unambiguous semidirect product(C11×#10596873)⋊C5

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC7×Dic7×C11⋊C5 ⋊ C3
HallC11⋊C5×#3861 ⋊ C4
HallC11×#10596873 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC7×C11×Dic7 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
HallC7×Dic7 ⋊ C3×C11⋊C5
Hall#3861 ⋊ C4×C11⋊C5
SylowC72 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C5×#10596873

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×#64423
commutator, hypocenterC72×C11C3×C4×C5
Fitting, socle, cosocleC2×C72×C11C2×C3×C5
prime radicalC2×C11⋊C5×#3861C2
LCSG ▷ C72×C11
UCSC1 ◁ C2

144 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 39 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) = 308

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 148);