Finite Group Databasebeta

C2×#14529767 #17038962

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14529767

Splittings

SylowC17 ⋊ C2×#1996

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC2×C17×#342C2
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C23
cosocleC24×C17C24
hypercenterC2×#342D17
hypocenterC17C2×#1996
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

1698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 174206);