Finite Group Databasebeta

C2×#14545112 #17978390

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14545112

Splittings

SylowC17 ⋊ C2×#2148

Subgroups

subgroupG/H
centerC22C2×#10587547
commutatorC8×C17C23×C4
FrattiniC8C23×#595
FittingC2×C17×#135C4
socleC22×C17C2×#102
prime radicalC2×#135×D17C2
cosocleC8×D17C24
hypercenterC2×#135#595
hypocenterC17C2×#2148
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

1154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113634);