Finite Group Databasebeta

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C2×C9×D799 #43273333

order28764
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D799
unambiguous semidirect product(C2×C17)⋊(C9×D47)
unambiguous semidirect product(C2×C47)⋊(C9×D17)

Splittings

FittingC2×C9×C17×C47 ⋊ C2
derived, HallC17×C47 ⋊ C22×C9
HallC9×C17×C47 ⋊ C22
HallC9×C47 ⋊ C2×D17
HallC9×C17 ⋊ C2×D47
SylowC47 ⋊ C2×C9×D17
SylowC17 ⋊ C2×C9×D47

Subgroups

subgroupG/H
center, hypercenterC2×C9D799
commutator, hypocenterC17×C47C22×C9
FrattiniC3C2×C3×D799
FittingC2×C9×C17×C47C2
socleC2×C3×C17×C47C2×C3
prime radicalC2×C3×D799C3
cosocleC3×C17×C47C22×C3
LCSG ▷ C17×C47
UCSC1 ◁ C2×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14382

Conjugacy classes & character table

7218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28764, 26);