Finite Group Databasebeta

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C3×(C49⋊C3)⋊Dic17 #44472402

order29988
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C49⋊C3)⋊Dic17
unambiguous semidirect product(C49⋊C3)⋊(C3×Dic17)
unambiguous semidirect productDic833⋊C32
unambiguous semidirect product(C3×Dic833)⋊C3

Splittings

derived, HallC17×C49 ⋊ C32×C4
HallC3×C17×C49⋊C3 ⋊ C4
HallDic833 ⋊ C32
HallC3×C49⋊C3 ⋊ Dic17
SylowC49 ⋊ C32×Dic17
SylowC17 ⋊ C3×(C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3C17⋊(D49⋊C3)
commutator, hypocenterC17×C49C32×C4
FrattiniC2×C7C3×C17⋊AGL(1,𝔽7)
FittingC2×C3×C17×C49C2×C3
socleC2×C3×C7×C17AGL(1,𝔽7)
prime radicalC2×C3×C17×C49⋊C3C2
cosocleC2×C17×C49C2×C32
LCSG ▷ C17×C49
UCSC1 ◁ C2×C3

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9996

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 43);