Finite Group Databasebeta

C22×#11762845 #17897972

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#11762845

Splittings

SylowC17 ⋊ C22×#427

Subgroups

subgroupG/H
centerC23×C4C22⋊D17
commutatorC4×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C17×#117C2
socleC24×C17C2×D4
prime radicalC25×C17D4
cosocleC2×C4×C17C25
hypercenterC22×#117D17
hypocenterC17C22×#427
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C22×#117

3006 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, 1033216);