Finite Group Databasebeta

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C11×Dic79⋊C9 #44530845

order31284
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic79⋊C9
unambiguous semidirect productDic79⋊(C9×C11)
unambiguous semidirect product(C79⋊C9)⋊(C4×C11)
unambiguous semidirect product(C11×Dic79)⋊C9

Splittings

derived, SylowC79 ⋊ C4×C9×C11
HallC11×C79⋊C9 ⋊ C4
HallC11×Dic79 ⋊ C9
HallC11×C79 ⋊ C4×C9
HallC79⋊C9 ⋊ C4×C11
HallDic79 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D79⋊C3
commutator, hypocenterC79C4×C9×C11
FrattiniC2×C3C11×D79⋊C3
Fitting, socle, prime radicalC2×C3×C11×C79C2×C3
cosocleC2×C3×C79C2×C3×C11
LCSG ▷ C79
UCSC1 ◁ C2×C3×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31284

Conjugacy classes & character table

1254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 10);