Finite Group Databasebeta

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C3×C5×C11⋊#5997 #44568803

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C11⋊#5997

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC72×C11 ⋊ C3×C4×C5
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ C4×C5
HallC3×C5×C72 ⋊ Dic11
HallC5×C72 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ #5997
HallC3×C72 ⋊ C5×Dic11
HallC5×C11 ⋊ C3×#5997
SylowC72 ⋊ C3×C5×Dic11
HallC3×C11 ⋊ C5×#5997
SylowC11 ⋊ C3×C5×#5997

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊#5997
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C5×C11×C7⋊D7C2
cosocleC11×C7⋊D7C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C3×C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 505);