Finite Group Databasebeta

#343×Dic17 #16939528

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#343×Dic17

Splittings

SylowC17 ⋊ C4×#343

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C17C43
FrattiniC23×C4C22×D17
FittingC2×C17×#343C2
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22×C4
cosocleC23×C4×C17C23
hypercenterC2×#343D17
hypocenterC17C4×#343
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 74772);