Finite Group Databasebeta

C4×#11762774 #17031849

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

Aliases

direct productC4×#11762774

Splittings

FittingC4×C17×C22⋊C8 ⋊ C2
SylowC17 ⋊ C4×#408

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC22×C17C22×C42
FrattiniC22×C4C23×D17
FittingC4×C17×C22⋊C8C2
socleC23×C17C23×C4
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenterC4×C22⋊C8D17
hypocenterC17C4×#408
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C4×C22⋊C8

1662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 167093);