Finite Group Databasebeta

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C32×(C11⋊C5)⋊#261 #38788024

order25740
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×(C11⋊C5)⋊#261
unambiguous semidirect product(C11⋊C5)⋊(C32×#261)
unambiguous semidirect product(C32×C11⋊#261)⋊C5

Splittings

Fitting, socle, HallC32×C11×C13 ⋊ C4×C5
derived, HallC11×C13 ⋊ C32×C4×C5
HallC32×C13×C11⋊C5 ⋊ C4
HallC32×C11⋊#261 ⋊ C5
HallC13×C11⋊C5 ⋊ C32×C4
HallC11⋊#261 ⋊ C32×C5
HallC32×C11⋊C5 ⋊ #261
HallC32×C13 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×#261
HallC11⋊C5 ⋊ C32×#261
SylowC13 ⋊ C32×Dic11⋊C5
SylowC11 ⋊ C32×C5×#261

Subgroups

subgroupG/H
center, hypercenterC32(C11⋊C5)⋊#261
commutator, hypocenterC11×C13C32×C4×C5
FrattiniC1G
Fitting, socleC32×C11×C13C4×C5
prime radicalC32×D13×C11⋊C5C2
cosocleC11×D13C2×C32×C5
LCSG ▷ C11×C13
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1287

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 255);