Finite Group Databasebeta

← Prev (#44477456) Next (#44477458) →

C2×C5×C9×D169 #44477457

order30420
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D169

Splittings

FittingC2×C5×C9×C169 ⋊ C2
derived, SylowC169 ⋊ C22×C5×C9
HallC5×C9×C169 ⋊ C22
HallC9×C169 ⋊ C22×C5
HallC5×C169 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D169
commutator, hypocenterC169C22×C5×C9
FrattiniC3×C13C2×C3×C5×D13
FittingC2×C5×C9×C169C2
socleC2×C3×C5×C13C3×D13
prime radicalC2×C3×C5×D169C3
cosocleC3×C169C22×C3×C5
LCSG ▷ C169
UCSC1 ◁ C2×C5×C9

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 46);