Finite Group Databasebeta

← Prev (#39907213) Next (#39907215) →

C5×C9×C17×D17 #39907214

order26010
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×C17×D17
unambiguous semidirect productC17⋊(C2×C5×C9×C17)

Splittings

Fitting, HallC5×C9×C172 ⋊ C2
derivedC17 ⋊ C2×C5×C9×C17
HallC9×C172 ⋊ C2×C5
HallC5×C172 ⋊ C2×C9
SylowC172 ⋊ C2×C5×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9×C17D17
commutator, hypocenterC17C2×C5×C9×C17
FrattiniC3C3×C5×C17×D17
FittingC5×C9×C172C2
socleC3×C5×C172C2×C3
prime radicalC3×C5×C17×D17C3
cosocleC3×C17C2×C3×C5×C17
LCSG ▷ C17
UCSC1 ◁ C5×C9×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1530

Conjugacy classes & character table

7650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26010, 28);