Finite Group Databasebeta

#455×#595 #17971215

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

Aliases

direct product#455×#595

Splittings

FittingC17×#455 ⋊ C4
SylowC17 ⋊ C4×#455

Subgroups

subgroupG/H
centerC2#120×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC17×#455C4
socleC2×C17C4×#120
prime radicalH(5,𝔽2)×D17C22
cosocleC2×C4×D17C24
hypercenter#455#595
hypocenterC17C4×#455
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

1442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1106459);