Finite Group Databasebeta

#131×#3624 #17963994

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#131×#3624

Splittings

SylowC17 ⋊ C8×#131

Subgroups

subgroupG/H
centerC2×C8C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC2×C4C23×#595
FittingC2×C17×#131C4
socleC22×C17C22×C42
prime radicalC2×#41×C17C2×C4
cosocleC4×Dic17C24
hypercenterC2×#131#595
hypocenterC17C8×#131
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×#131

922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1099238);