Finite Group Databasebeta

C4×#11762572 #16939505

order4352
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11762572

Splittings

SylowC17 ⋊ C4×#340

Subgroups

subgroupG/H
centerC23×C4D68
commutatorC4×C17C43
FrattiniC23×C4C22×D17
FittingC22×C4×C8×C17C2
socle, prime radicalC24×C17C2×D4
cosocleC23×C4×C17C23
hypercenterC22×C4×C8D17
hypocenterC17C4×#340
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 74749);