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C5×C3⋊(C3⋊(C11⋊#261)) #38788260

order25740
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊(C3⋊(C11⋊#261))
unambiguous semidirect productC3⋊(C5×C3⋊(C11⋊#261))

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derived, HallC32×C11×C13 ⋊ C4×C5
HallC5×C11×C13 ⋊ C3⋊Dic3
HallC32×C5×C13 ⋊ Dic11
HallC32×C5×C11 ⋊ #261
HallC11×C13 ⋊ C5×C3⋊Dic3
HallC32×C13 ⋊ C5×Dic11
HallC32×C11 ⋊ C5×#261
HallC5×C13 ⋊ C3⋊Dic33
HallC5×C11 ⋊ C3⋊(C3⋊#261)
HallC32×C5 ⋊ C11⋊#261
SylowC13 ⋊ C5×C3⋊Dic33
SylowC11 ⋊ C5×C3⋊(C3⋊#261)
SylowC32 ⋊ C5×C11⋊#261

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊(C11⋊#261))
commutator, hypocenterC32×C11×C13C4×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C5×C11×D13C2
cosocleC32×C11×D13C2×C5
LCSG ▷ C32×C11×C13
UCSC1 ◁ C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6435

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 491);