Finite Group Databasebeta

#350×Dic17 #16949374

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#350×Dic17

Splittings

SylowC17 ⋊ C4×#350

Subgroups

subgroupG/H
centerC2×C8D4×D17
commutatorC4×C17C2×C4×C8
FrattiniC22×C8C22×D17
FittingC2×C17×#350C2
socleC22×C17C2×C22⋊C8
prime radicalC2×#41×C17C2×C4
cosocleC22×C8×C17C23
hypercenterC2×#350D17
hypocenterC17C4×#350
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84618);