Finite Group Databasebeta

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C11⋊C5×#10596874 #44568442

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

Aliases

direct productC11⋊C5×#10596874
unambiguous semidirect product(C11×#10596874)⋊C5

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC11⋊C5×C7⋊Dic7 ⋊ C3
HallC11⋊C5×#3861 ⋊ C4
HallC11×#10596874 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC11×C7⋊Dic7 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
HallC7⋊Dic7 ⋊ C3×C11⋊C5
Hall#3861 ⋊ C4×C11⋊C5
SylowC72 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C5×#10596874

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×#64424
commutator, hypocenterC72×C11C3×C4×C5
Fitting, socle, cosocleC2×C72×C11C2×C3×C5
prime radicalC2×C11⋊C5×#3861C2
LCSG ▷ C72×C11
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 144);