Finite Group Databasebeta

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C5×A4×C563 #46798709

order33780
automorphism?
homologyAbelianization (H1) = C3×C5×C563 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C563
unambiguous semidirect productC22⋊(C3×C5×C563)
unambiguous semidirect product(C22×C5)⋊(C3×C563)
unambiguous semidirect product(C22×C563)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C563)⋊C3

Splittings

Fitting, socle, HallC22×C5×C563 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C563
HallC22×C563 ⋊ C3×C5
HallC22×C5 ⋊ C3×C563

Subgroups

subgroupG/H
center, hypercenterC5×C563A4
commutator, cosocle, hypocenterC22C3×C5×C563
FrattiniC1G
Fitting, socleC22×C5×C563C3
LCSG ▷ C22
UCSC1 ◁ C5×C563

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11260

Conjugacy classes & character table

11260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33780, 21);