Finite Group Databasebeta

C4×#11762531 #16923673

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C43

Aliases

direct productC4×#11762531

Splittings

SylowC17 ⋊ C4×#322

Subgroups

subgroupG/H
centerC43C2×D17
commutatorC2×C17C42×C8
FrattiniC2×C42C22×D17
FittingC42×C8×C17C2
socle, prime radicalC23×C17C2×C42
cosocleC2×C42×C17C23
hypercenterC42×C8D17
hypocenterC17C4×#322
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C43 ◁ C42×C8

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 58917);