Finite Group Databasebeta

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C3×C43×#63118 #46776546

order33540
automorphism?
homologyAbelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C1

Aliases

direct productC3×C43×#63118

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C4
derived, HallC5×C13 ⋊ C3×C4×C43
HallC5×C13×C43 ⋊ C3×C4
HallC3×C13×C43 ⋊ Dic5
HallC3×C5×C43 ⋊ #261
HallC13×C43 ⋊ C3×Dic5
HallC5×C43 ⋊ C3×#261
HallC3×C5×C13 ⋊ C4×C43
HallC3×C13 ⋊ Dic5×C43
HallC3×C5 ⋊ C43×#261
SylowC13 ⋊ C3×Dic5×C43
SylowC5 ⋊ C3×C43×#261

Subgroups

subgroupG/H
center, hypercenterC3×C43#63118
commutator, hypocenterC5×C13C3×C4×C43
FrattiniC1G
Fitting, socleC3×C5×C13×C43C4
prime radicalC3×C5×D13×C43C2
cosocleC5×D13C2×C3×C43
LCSG ▷ C5×C13
UCSC1 ◁ C3×C43

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

2967 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 166);