Finite Group Databasebeta

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C9×D17×C121 #49150044

order37026
automorphism?
homologyAbelianization (H1) = C2×C9×C121 · Schur multiplier (H2) = C1

Aliases

direct productC9×D17×C121
unambiguous semidirect productC17⋊(C2×C9×C121)

Splittings

Fitting, HallC9×C17×C121 ⋊ C2
derived, SylowC17 ⋊ C2×C9×C121
HallC17×C121 ⋊ C2×C9
HallC9×C17 ⋊ C2×C121

Subgroups

subgroupG/H
center, hypercenterC9×C121D17
commutator, hypocenterC17C2×C9×C121
FrattiniC3×C11C3×C11×D17
FittingC9×C17×C121C2
socle, cosocleC3×C11×C17C2×C3×C11
prime radicalC3×C11×D17C3×C11
LCSG ▷ C17
UCSC1 ◁ C9×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18513

Conjugacy classes & character table

10890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37026, 2);