Finite Group Databasebeta

C2×#14526865 #16949176

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526865

Splittings

SylowC17 ⋊ C2×#1376

Subgroups

subgroupG/H
centerC22×C8C22⋊D17
commutatorC4×C17C2×C4×C8
FrattiniC22×C8C22×D17
FittingC22×C17×M32C2
socleC23×C17C4⋊C8
prime radicalC24×C17M16
cosocleC22×C8×C17C23
hypercenterC22×M32D17
hypocenterC17C2×#1376
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×M32

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 84420);