Finite Group Databasebeta

← Prev (#42123786) Next (#42123788) →

C2×C17×#11717941 #42123787

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

Aliases

direct productC2×C17×#11717941

Splittings

derived, HallC7×C13 ⋊ C2×C9×C17
HallC2×C7×C13×C17 ⋊ C9
HallC7×C13×C17 ⋊ C2×C9
HallC2×C13×C17 ⋊ C7⋊C9
HallC2×C7×C17 ⋊ C13⋊C9
HallC13×C17 ⋊ C2×C7⋊C9
HallC2×C7×C13 ⋊ C9×C17
HallC7×C17 ⋊ C2×C13⋊C9
HallC2×C13 ⋊ C17×C7⋊C9
HallC2×C7 ⋊ C17×C13⋊C9
SylowC13 ⋊ C2×C17×C7⋊C9
SylowC7 ⋊ C2×C17×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17#63270
commutator, hypocenterC7×C13C2×C9×C17
FrattiniC3C2×C17×#63270
Fitting, socle, prime radicalC2×C3×C7×C13×C17C3
cosocleC3×C7×C13C2×C3×C17
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 27846

Conjugacy classes & character table

3366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27846, 4);