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C2×C4×3−1+2⋊C8 #13142427

order1728
isoclinismisoclinic class of AGL(1,ℤ/9)
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×3−1+2⋊C8
unambiguous semidirect product(C2×C4×C9⋊C8)⋊C3

Splittings

derivedC9 ⋊ C2×C3×C4×C8
Sylow3−1+2 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C42AGL(1,ℤ/9)
commutator, hypocenterC9C2×C3×C4×C8
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C42×3−1+2C2
socleC23×C3C2×C3×Dic3
prime radicalC23×C32C2×Dic3
cosocleC2×C4×C9C23×C3
LCSG ▷ C9
UCSC1 ◁ C2×C42

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8490);