Finite Group Databasebeta

C4×#11762579 #16939532

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#11762579

Splittings

SylowC17 ⋊ C4×#344

Subgroups

subgroupG/H
centerC42#63227
commutatorC22×C17C43
FrattiniC23×C4C22×D17
FittingC4×C17×#117C2
socleC22×C17C2×#95
prime radicalC24×C17C22×C4
cosocleC23×C4×C17C23
hypercenterC4×#117D17
hypocenterC17C4×#344
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C22×C42 ◁ C4×#117

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 74776);