Finite Group Databasebeta

C4×#11762743 #16956162

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11762743

Splittings

SylowC17 ⋊ C4×#398

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC4×C17×#95C2
socle, prime radical, cosocleC24×C17C24
hypercenterC4×#95D17
hypocenterC17C4×#398
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C4×#95

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 91406);