Finite Group Databasebeta

C4×#11763868 #17978140

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11763868

Splittings

SylowC17 ⋊ C4×#504

Subgroups

subgroupG/H
centerC42C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC2×C4C23×#595
FittingC4×M16×C17C4
socleC22×C17C23×C8
prime radicalC2×#63252C2×C4
cosocleC2×#3622C24
hypercenterC4×M16#595
hypocenterC17C4×#504
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C4×M16

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113384);