Finite Group Databasebeta

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C2×C4×C5×C22⋊C9 #13085305

order1440
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C9 · Schur multiplier (H2) = C22

Aliases

direct productC2×C4×C5×C22⋊C9
unambiguous semidirect product(C23×C4)⋊(C5×C9)
unambiguous semidirect product(C23×C4×C5)⋊C9

Splittings

derivedC22 ⋊ C2×C4×C5×C9
HallC23×C4×C5 ⋊ C9
SylowC23×C4 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4×C5A4
commutator, hypocenterC22C2×C4×C5×C9
FrattiniC2×C3C22×C5×A4
FittingC23×C3×C4×C5C3
socle, prime radicalC24×C3×C5C2×C3
cosocleC23×C3C22×C3×C5
LCSG ▷ C22
UCSC1 ◁ C2×C3×C4×C5

232 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 360

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1622);