Finite Group Databasebeta

C9×C17×D91 #42123794

order27846
automorphism?
homologyAbelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC9×C17×D91

Splittings

Fitting, HallC7×C9×C13×C17 ⋊ C2
derived, HallC7×C13 ⋊ C2×C9×C17
HallC9×C13×C17 ⋊ D7
HallC7×C13×C17 ⋊ C2×C9
HallC7×C9×C17 ⋊ D13
HallC7×C9×C13 ⋊ C2×C17
HallC13×C17 ⋊ C9×D7
HallC7×C17 ⋊ C9×D13
HallC9×C13 ⋊ D7×C17
HallC7×C9 ⋊ C17×D13
SylowC13 ⋊ C9×D7×C17
SylowC7 ⋊ C9×C17×D13

Subgroups

subgroupG/H
center, hypercenterC9×C17D91
commutator, hypocenterC7×C13C2×C9×C17
FrattiniC3C3×C17×D91
FittingC7×C9×C13×C17C2
socleC3×C7×C13×C17C2×C3
prime radicalC3×C17×D91C3
cosocleC3×C7×C13C2×C3×C17
LCSG ▷ C7×C13
UCSC1 ◁ C9×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13923

Conjugacy classes & character table

7191 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27846, 11);