Finite Group Databasebeta

#323×Dic17 #16924828

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#323×Dic17

Splittings

SylowC17 ⋊ C4×#323

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC22×C17C2×C4×C8
FrattiniC23×C4C22×D17
FittingC2×C17×#323C2
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×C4×C17C23
hypercenterC2×#323D17
hypocenterC17C4×#323
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 60072);