Finite Group Databasebeta

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C9×C17×#5997 #44472589

order29988
automorphism?
homologyAbelianization (H1) = C4×C9×C17 · Schur multiplier (H2) = C7

Aliases

direct productC9×C17×#5997

Splittings

Fitting, HallC72×C9×C17 ⋊ C4
derived, SylowC72 ⋊ C4×C9×C17
HallC72×C17 ⋊ C4×C9
HallC72×C9 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC9×C17#5997
commutator, hypocenterC72C4×C9×C17
FrattiniC3C3×C17×#5997
FittingC72×C9×C17C4
socleC3×C72×C17C3×C4
prime radicalC3×C17×C7⋊D7C2×C3
cosocleC3×C7⋊D7C2×C3×C17
LCSG ▷ C72
UCSC1 ◁ C9×C17

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2142

Conjugacy classes & character table

2448 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 230);