Finite Group Databasebeta

C4×#11763608 #17898408

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#11763608

Splittings

FittingC4×C17×#137 ⋊ C2
SylowC17 ⋊ C4×#575

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC4×C17×#137C2
socleC22×C17C23×D4
prime radicalC2×#11763608C2
cosocleC2×C4×C17C25
hypercenterC4×#137D17
hypocenterC17C4×#575
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

2842 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, 1033652);