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C5×#20269439 #46776407

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

Aliases

direct productC5×#20269439

Splittings

derived, HallC13×C43 ⋊ C3×C4×C5
HallC5×C43×Dic13 ⋊ C3
HallC5×#13131976 ⋊ C4
HallC5×C13×C43 ⋊ C3×C4
HallC43×Dic13 ⋊ C3×C5
Hall#13131976 ⋊ C4×C5
HallC5×Dic13 ⋊ C43⋊C3
HallC5×C43 ⋊ Dic13⋊C3
HallC5×C13 ⋊ C4×C43⋊C3
HallDic13 ⋊ C5×C43⋊C3
SylowC43 ⋊ C5×Dic13⋊C3
SylowC13 ⋊ C4×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#16809813
commutator, hypocenterC13×C43C3×C4×C5
FrattiniC2C5×#16809813
Fitting, socleC2×C5×C13×C43C2×C3
prime radicalC2×C5×#13131976C2
cosocleC2×C13×C43C2×C3×C5
LCSG ▷ C13×C43
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11180

Conjugacy classes & character table

1200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 27);