Finite Group Databasebeta

#533×#595 #17978906

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#533×#595

Splittings

FittingC17×#533 ⋊ C4
SylowC17 ⋊ C4×#533

Subgroups

subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC17×#533C4
prime radicalC23×D17C24
cosocleC22×D17C25
hypercenter#533#595
hypocenterC17C4×#533
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #533

2550 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, 1114150);