Finite Group Databasebeta

C22×#11762643 #17192430

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11762643

Splittings

SylowC17 ⋊ C22×M64

Subgroups

subgroupG/H
centerC22×C16C2×D17
commutatorC2×C17C23×C16
FrattiniC16C23×D17
FittingC23×C16×C17C2
socleC23×C17C2×C16
prime radicalC24×C17C16
cosocleC16×C17C24
hypercenterC23×C16D17
hypocenterC17C22×M64
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C16 ◁ C23×C16

502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327674);