Finite Group Databasebeta

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C17×#157×C49 #44472469

order29988
automorphism?
homologyAbelianization (H1) = C4×C17×C49 · Schur multiplier (H2) = C3

Aliases

direct productC17×#157×C49

Splittings

Fitting, HallC32×C17×C49 ⋊ C4
derived, SylowC32 ⋊ C4×C17×C49
HallC32×C49 ⋊ C4×C17
HallC32×C17 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC17×C49#157
commutator, hypocenterC32C4×C17×C49
FrattiniC7C7×C17×#157
FittingC32×C17×C49C4
socleC32×C7×C17C4×C7
prime radicalC7×C17×C3⋊D3C2×C7
cosocleC7×C3⋊D3C2×C7×C17
LCSG ▷ C32
UCSC1 ◁ C17×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4998

Conjugacy classes & character table

4998 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 110);