Finite Group Databasebeta

#554×#595 #17979034

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

Aliases

direct product#554×#595

Splittings

FittingC17×#554 ⋊ C4
SylowC17 ⋊ C4×#554

Subgroups

subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#554C4
prime radicalC2×D4×D17C23
cosocleC22×D17C25
hypercenter#554#595
hypocenterC17C4×#554
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #554

2516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114278);