Finite Group Databasebeta

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C9×Dic11×C79 #44530839

order31284
automorphism?
homologyAbelianization (H1) = C4×C9×C79 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic11×C79
unambiguous semidirect productC11⋊(C4×C9×C79)

Splittings

derived, SylowC11 ⋊ C4×C9×C79
HallC9×C11×C79 ⋊ C4
HallC11×C79 ⋊ C4×C9
HallC9×C11 ⋊ C4×C79

Subgroups

subgroupG/H
center, hypercenterC2×C9×C79D11
commutator, hypocenterC11C4×C9×C79
FrattiniC2×C3C3×D11×C79
FittingC2×C9×C11×C79C2
socle, prime radicalC2×C3×C11×C79C2×C3
cosocleC2×C3×C11C2×C3×C79
LCSG ▷ C11
UCSC1 ◁ C2×C9×C79

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31284

Conjugacy classes & character table

9954 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 4);