Finite Group Databasebeta

#357×Dic17 #16949530

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct product#357×Dic17

Splittings

SylowC17 ⋊ C4×#357

Subgroups

subgroupG/H
centerC23D8×D17
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC2×C17×#357C2
socleC23×C17C2×D8
prime radicalC22×D8×C17C22
cosocleC22×C8×C17C23
hypercenterC2×#357D17
hypocenterC17C4×#357
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

534 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, 84774);