Finite Group Databasebeta

C2×C4×#10587502 #16955393

order4352
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×C4×#10587502

Splittings

SylowC17 ⋊ C2×C4×#95

Subgroups

subgroupG/H
centerC24×C4C2×D17
commutatorC2×C17C2×C43
FrattiniC24C23×D17
FittingC23×C42×C17C2
socle, prime radicalC25×C17C23
cosocleC24×C17C24
hypercenterC23×C42D17
hypocenterC17C2×C4×#95
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24×C4 ◁ C23×C42

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 90637);