Finite Group Databasebeta

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C3×C5×C43⋊#261 #46776535

order33540
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C43⋊#261

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C4
derived, HallC13×C43 ⋊ C3×C4×C5
HallC5×C13×C43 ⋊ C3×C4
HallC3×C13×C43 ⋊ C4×C5
HallC3×C5×C43 ⋊ #261
HallC5×C43 ⋊ C3×#261
HallC3×C5×C13 ⋊ Dic43
HallC3×C43 ⋊ C5×#261
HallC5×C13 ⋊ C3×Dic43
SylowC43 ⋊ C3×C5×#261
HallC3×C13 ⋊ C5×Dic43
SylowC13 ⋊ C3×C5×Dic43

Subgroups

subgroupG/H
center, hypercenterC3×C5C43⋊#261
commutator, hypocenterC13×C43C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C43C4
prime radicalC3×C5×D13×C43C2
cosocleD13×C43C2×C3×C5
LCSG ▷ C13×C43
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

2625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 155);