Finite Group Databasebeta

#448×#595 #17971176

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

Aliases

direct product#448×#595

Splittings

FittingC17×#448 ⋊ C4
SylowC17 ⋊ C4×#448

Subgroups

subgroupG/H
centerC22C2×D4×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC17×#448C4
socleC22×C17C2×C4×D4
prime radical#121×D17C22
cosocleC2×C4×D17C24
hypercenter#448#595
hypocenterC17C4×#448
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

1532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1106420);