Finite Group Databasebeta

C4×#11762738 #16956146

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#11762738

Splittings

FittingC4×C17×#95 ⋊ C2
SylowC17 ⋊ C4×#397

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC4×C17×#95C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenterC4×#95D17
hypocenterC17C4×#397
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C4×#95

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 91390);