Finite Group Databasebeta

C2×C4×C9×C3⋊C8 #13142371

order1728
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C4×C8×C9 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×C9×C3⋊C8

Splittings

derivedC3 ⋊ C2×C4×C8×C9
SylowC3×C9 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C42×C9D3
commutator, hypocenterC3C2×C4×C8×C9
FrattiniC2×C3×C4C22×C3×D3
FittingC2×C3×C42×C9C2
socle, prime radicalC23×C32C2×C3×C4
cosocleC2×C32×C4C23×C3
LCSG ▷ C3
UCSC1 ◁ C2×C42×C9

594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 8434);