Finite Group Databasebeta

C2×#14529296 #17036252

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#14529296

Splittings

FittingC22×C17×#101 ⋊ C2
SylowC17 ⋊ C2×#1908

Subgroups

subgroupG/H
centerC23#10587570
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#101C2
socleC23×C17#121
prime radicalC22×#63252C22
cosocleC22×C4×C17C24
hypercenterC22×#101D17
hypocenterC17C2×#1908
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171496);