Finite Group Databasebeta

C2×#14526604 #16922254

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14526604

Splittings

FittingC2×C17×#336 ⋊ C2
SylowC17 ⋊ C2×#1270

Subgroups

subgroupG/H
centerC24#63227
commutatorC2×C4×C17C22×C8
FrattiniC2×C42C22×D17
FittingC2×C17×#336C2
socleC24×C17C22⋊C4
prime radicalC23×D68C4
cosocleC2×C42×C17C23
hypercenterC2×#336D17
hypocenterC17C2×#1270
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 57498);