Finite Group Databasebeta

C2×#14545222 #17978859

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14545222

Splittings

FittingC22×C4⋊C4×C17 ⋊ C4
SylowC17 ⋊ C2×#2274

Subgroups

subgroupG/H
centerC23C23×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#2274
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4⋊C4

4110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114103);