Finite Group Databasebeta

C2×#14528549 #17031839

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14528549

Splittings

FittingC2×C17×#336 ⋊ C2
SylowC17 ⋊ C2×#1750

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C22×C42
FrattiniC22×C4C23×D17
FittingC2×C17×#336C2
socleC24×C17C22×C4
prime radicalC24×D17C2×C4
cosocleC22×C4×C17C24
hypercenterC2×#336D17
hypocenterC17C2×#1750
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×#336

1766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 167083);