Finite Group Databasebeta

C22×#11762555 #17002607

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11762555

Splittings

SylowC17 ⋊ C22×#332

Subgroups

subgroupG/H
centerC24C22⋊Dic17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC22×C17×C4⋊Q8C2
socle, prime radicalC24×C17C22⋊C4
cosocleC42×C17C24
hypercenterC22×C4⋊Q8D17
hypocenterC17C22×#332
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

1334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 137851);