Finite Group Databasebeta

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C5×A4×C569 #46802490

order34140
automorphism?
homologyAbelianization (H1) = C3×C5×C569 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C569
unambiguous semidirect productC22⋊(C3×C5×C569)
unambiguous semidirect product(C22×C5)⋊(C3×C569)
unambiguous semidirect product(C22×C569)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C569)⋊C3

Splittings

Fitting, socle, HallC22×C5×C569 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C569
HallC22×C569 ⋊ C3×C5
HallC22×C5 ⋊ C3×C569

Subgroups

subgroupG/H
center, hypercenterC5×C569A4
commutator, cosocle, hypocenterC22C3×C5×C569
FrattiniC1G
Fitting, socleC22×C5×C569C3
LCSG ▷ C22
UCSC1 ◁ C5×C569

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11380

Conjugacy classes & character table

11380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34140, 29);