Finite Group Databasebeta

C4×#11762772 #17031867

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11762772

Splittings

FittingC2×C4×M16×C17 ⋊ C2
SylowC17 ⋊ C4×#407

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC22×C17C22×C42
FrattiniC22×C4C23×D17
FittingC2×C4×M16×C17C2
socleC23×C17C23×C4
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenterC2×C4×M16D17
hypocenterC17C4×#407
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

2246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167111);