Finite Group Databasebeta

C2×#14526925 #16954530

order4352
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14526925

Splittings

FittingC22×C17×C32 ⋊ C2
SylowC17 ⋊ C2×#1401

Subgroups

subgroupG/H
centerC2×C16D68
commutatorC4×C17C22×C16
FrattiniC2×C16C22×D17
FittingC22×C17×C32C2
socleC22×C17C22⋊C16
prime radicalC2×#63252C8
cosocleC2×C16×C17C23
hypercenterC22×C32D17
hypocenterC17C2×#1401
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C16 ◁ C22×C16 ◁ C22×C32

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 89774);