Finite Group Databasebeta

#365×Dic17 #16949710

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

Aliases

direct product#365×Dic17

Splittings

SylowC17 ⋊ C4×#365

Subgroups

subgroupG/H
centerC22#106×D17
commutatorC8×C17C2×C42
FrattiniC22×C8C22×D17
FittingC2×C17×#365C2
socleC22×C17C2×#106
prime radicalC23×C17C2×SD16
cosocleC22×C8×C17C23
hypercenterC2×#365D17
hypocenterC17C4×#365
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 84954);