Finite Group Databasebeta

C2×#14544992 #17978127

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14544992

Splittings

FittingC22×C16×C17 ⋊ C4
SylowC17 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC2×C16C2×#595
commutatorC2×C17C22×C4×C8
FrattiniC8C23×#595
FittingC22×C16×C17C4
socleC22×C17C2×C4×C8
prime radicalC23×D17C2×C8
cosocleC8×D17C24
hypercenterC22×C16#595
hypocenterC17C2×#2108
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C16 ◁ C22×C16

854 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, 1113371);