Finite Group Databasebeta

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C5×C3⋊(C11⋊#5997) #44568838

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

Aliases

direct productC5×C3⋊(C11⋊#5997)
unambiguous semidirect productC3⋊(C5×C11⋊#5997)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC3×C72×C11 ⋊ C4×C5
HallC5×C72×C11 ⋊ Dic3
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ C5×Dic3
HallC5×C72 ⋊ Dic33
HallC3×C5×C11 ⋊ #5997
HallC3×C72 ⋊ C5×Dic11
HallC5×C11 ⋊ C3⋊#5997
SylowC72 ⋊ C5×Dic33
HallC3×C11 ⋊ C5×#5997
HallC3×C5 ⋊ C11⋊#5997
SylowC11 ⋊ C5×C3⋊#5997
SylowC3 ⋊ C5×C11⋊#5997

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C11⋊#5997)
commutator, hypocenterC3×C72×C11C4×C5
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C5×C11×C7⋊D7C2
cosocleC3×C11×C7⋊D7C2×C5
LCSG ▷ C3×C72×C11
UCSC1 ◁ C5

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 540);