Finite Group Databasebeta

#334×Dic17 #16925507

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#334×Dic17

Splittings

SylowC17 ⋊ C4×#334

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C2×C4×C8
FrattiniC2×C42C22×D17
FittingC2×C17×#334C2
socle, prime radicalC23×C17C2×C4⋊C4
cosocleC2×C42×C17C23
hypercenterC2×#334D17
hypocenterC17C4×#334
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 60751);