Finite Group Databasebeta

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C5×A4×C263 #30628875

order15780
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C5×C263 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C263
unambiguous semidirect productC22⋊(C3×C5×C263)
unambiguous semidirect product(C22×C5)⋊(C3×C263)
unambiguous semidirect product(C22×C263)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C263)⋊C3

Splittings

Fitting, socle, HallC22×C5×C263 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C263
HallC22×C263 ⋊ C3×C5
HallC22×C5 ⋊ C3×C263

Subgroups

subgroupG/H
center, hypercenterC5×C263A4
commutator, cosocle, hypocenterC22C3×C5×C263
FrattiniC1G
Fitting, socleC22×C5×C263C3
LCSG ▷ C22
UCSC1 ◁ C5×C263

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5260

Conjugacy classes & character table

5260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15780, 21);