Finite Group Databasebeta

C4×#11762814 #17032101

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#11762814

Splittings

SylowC17 ⋊ C4×#418

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D17
commutatorC4×C17C22×C42
FrattiniC22×C4C23×D17
FittingC22×C4×D4×C17C2
socleC23×C17C22×D4
prime radicalC23×D4×C17C22
cosocleC22×C4×C17C24
hypercenterC22×C4×D4D17
hypocenterC17C4×#418
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×D4

2018 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, 167345);