Finite Group Databasebeta

C2×#14528554 #17031891

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#14528554

Splittings

FittingC2×C17×#336 ⋊ C2
SylowC17 ⋊ C2×C8×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC2×C17C22×C4×C8
FrattiniC22×C4C23×D17
FittingC2×C17×#336C2
socleC24×C17C22×C4
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenterC2×#336D17
hypocenterC17C2×C8×C22⋊C4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×#336

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 167135);