Finite Group Databasebeta

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C3×Dic17×C49⋊C3 #44472403

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

Aliases

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

Splittings

derived, HallC17×C49 ⋊ C32×C4
HallC3×C17×C49⋊C3 ⋊ C4
HallC49×Dic17 ⋊ C32
SylowC49 ⋊ C32×Dic17
SylowC17 ⋊ C3×C4×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D17×C49⋊C3
commutator, hypocenterC17×C49C32×C4
FrattiniC2×C7C3×ΓL(1,𝔽8)×D17
FittingC2×C3×C17×C49C2×C3
socleC2×C3×C7×C17C2×ΓL(1,𝔽8)
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

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 44);