Finite Group Databasebeta

#442×Dic17 #17032808

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct product#442×Dic17

Splittings

SylowC17 ⋊ C4×#442

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutatorC4×C17C22×C42
FrattiniC22×C4C23×D17
FittingC2×C17×#442C2
socleC23×C17C22×D4
prime radicalC22×D8×C17C22
cosocleC22×C4×C17C24
hypercenterC2×#442D17
hypocenterC17C4×#442
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

1326 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, 168052);