Finite Group Databasebeta

#532×#595 #17978905

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#532×#595

Splittings

FittingC17×#532 ⋊ C4
SylowC17 ⋊ C4×#532

Subgroups

subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC17×#532C4
prime radicalD17×#532C2
cosocleC22×D17C25
hypercenter#532#595
hypocenterC17C4×#532
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #532

3526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114149);