Finite Group Databasebeta

C4×#11762665 #16955532

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#11762665

Splittings

SylowC17 ⋊ C4×#379

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C22×C42
FrattiniC24C23×D17
FittingC25×C4×C17C2
socle, cosocleC24×C17C24
prime radicalC26×C17C22
hypercenterC25×C4D17
hypocenterC17C4×#379
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C25×C4

6734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90776);