Finite Group Databasebeta

C2×#14543868 #17960565

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14543868

Splittings

FittingC24×C4×C17 ⋊ C4
SylowC17 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC23#10587551
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC24×C4×C17C4
socleC23×C17#99
prime radicalC23×C22⋊D17C22
cosocleC22×C22⋊D17C23
hypercenterC24×C4#595
hypocenterC17C2×#1390
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24 ◁ C25 ◁ C24×C4

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095809);