Finite Group Databasebeta

C4×#11763392 #17193387

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#11763392

Splittings

FittingC42×D4×C17 ⋊ C2
SylowC17 ⋊ C4×#538

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC42×D4×C17C2
socle, cosocleC23×C17C25
prime radicalC2×#11763392C2
hypercenterC42×D4D17
hypocenterC17C4×#538
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C42×D4

2650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328631);