Finite Group Databasebeta

C2×#14544844 #17970126

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14544844

Splittings

SylowC17 ⋊ C2×#1917

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC23×C17C23×C4
FrattiniC23C23×#595
FittingC22×C4⋊C4×C17C4
socle, prime radicalC24×C17C22×C4
cosocleC22×Dic17C24
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#1917
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C4⋊C4

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105370);