Finite Group Databasebeta

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C11⋊C5×#5997⋊C3 #44568544

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

Aliases

direct productC11⋊C5×#5997⋊C3
unambiguous semidirect product#5997⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×#5997⋊C3)⋊C5
unambiguous semidirect product(C11⋊C5×#5997)⋊C3

Splittings

Fitting, socle, derived, HallC72×C11 ⋊ C3×C4×C5
HallC11⋊C5×#5997 ⋊ C3
HallC11⋊C5×#3861 ⋊ C4
HallC11×#5997⋊C3 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC11×#5997 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
Hall#5997 ⋊ C3×C11⋊C5
Hall#3861 ⋊ C4×C11⋊C5
SylowC72 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C5×#5997⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C11C3×C4×C5
prime radicalC11⋊C5×#64424C2
cosocleC11×C7⋊D7C2×C3×C5
LCSG ▷ C72×C11
UCSC1

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 154

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 246);