Finite Group Databasebeta

#331×Dic17 #16925266

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

Aliases

direct product#331×Dic17

Splittings

SylowC17 ⋊ C4×#331

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC2×C4×C17C2×C42
FrattiniC2×C42C22×D17
FittingC2×C17×#331C2
socleC23×C17C2×C22⋊C4
prime radicalC2×C17×#127C22
cosocleC2×C42×C17C23
hypercenterC2×#331D17
hypocenterC17C4×#331
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

708 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60510);