Finite Group Databasebeta

#585×Dic17 #17940939

order4352
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct product#585×Dic17

Splittings

SylowC17 ⋊ C4×#585

Subgroups

subgroupG/H
centerC2×C4C24×D17
commutatorC2×C17C25×C4
FrattiniC22C25×D17
Fitting, prime radicalC2×C17×#585C2
socle, cosocleC22×C17C26
hypercenterC2×#585D17
hypocenterC17C4×#585
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#585

11346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076183);