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C5×A4×C22⋊C8 #14510951

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C23

Aliases

direct productC5×A4×C22⋊C8
unambiguous semidirect product(C22×C22⋊C8)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C22⋊C8)⋊C3

Splittings

Fitting, HallC22×C5×C22⋊C8 ⋊ C3
SylowC22×C22⋊C8 ⋊ C3×C5

Subgroups

subgroupG/H
centerC2×C4×C5C22×A4
commutatorC23C2×C3×C5×C8
FrattiniC2×C4C22×C5×A4
FittingC22×C5×C22⋊C8C3
socleC24×C5C2×C3×C4
prime radicalC23×C5×A4C4
cosocleC23×C4C22×C3×C5
hypercenterC5×C22⋊C8A4
hypocenterC22C3×C5×C22⋊C8
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C2×C4×C5 ◁ C5×C22⋊C8

524 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236649);