Finite Group Databasebeta

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C9×C17×#595 #23780842

order10404
isoclinismisoclinic class of #595
automorphism?
homologyAbelianization (H1) = C4×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC9×C17×#595

Splittings

Fitting, HallC9×C172 ⋊ C4
derivedC17 ⋊ C4×C9×C17
SylowC172 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC9×C17#595
commutator, hypocenterC17C4×C9×C17
FrattiniC3C3×C17×#595
FittingC9×C172C4
socleC3×C172C3×C4
prime radicalC3×C17×D17C2×C3
cosocleC3×D17C2×C3×C17
LCSG ▷ C17
UCSC1 ◁ C9×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10404, 52);