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C11⋊C5×C3⋊#5997 #44568592

order32340
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC11⋊C5×C3⋊#5997
unambiguous semidirect productC3⋊(C11⋊C5×#5997)
unambiguous semidirect product(C11×C3⋊#5997)⋊C5

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C4×C5
HallC3×C72×C11⋊C5 ⋊ C4
HallC11×C3⋊#5997 ⋊ C5
HallC72×C11⋊C5 ⋊ Dic3
HallC72×C11 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ #5997
HallC3×C72 ⋊ C4×C11⋊C5
SylowC72 ⋊ Dic3×C11⋊C5
HallC3×C11 ⋊ C5×#5997
SylowC11 ⋊ C5×C3⋊#5997
SylowC3 ⋊ C11⋊C5×#5997

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C72×C11C4×C5
prime radicalC3×C11⋊C5×C7⋊D7C2
cosocleC3×C11×C7⋊D7C2×C5
LCSG ▷ C3×C72×C11
UCSC1

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 294);