Finite Group Databasebeta

C2×#14530388 #17186981

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

Aliases

direct productC2×#14530388

Splittings

SylowC17 ⋊ C2×#2110

Subgroups

subgroupG/H
centerC2×C8C4×Dic17
commutatorC4×C17C22×C42
FrattiniC2×C8C23×D17
FittingC22×C17×M32C2
socleC22×C17C2×#97
prime radicalC24×C17M16
cosocleC2×C8×C17C24
hypercenterC22×M32D17
hypocenterC17C2×#2110
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×M32

738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322225);