Finite Group Databasebeta

C2×#14544505 #17968266

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC2×#14544505

Splittings

FittingC2×C4×C8×C17 ⋊ C4
SylowC17 ⋊ C2×#1747

Subgroups

subgroupG/H
centerC2×C8C4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC22×C17#376
prime radicalC23×D17#41
cosocleC2×C4×D17C24
hypercenterC2×C4×C8#595
hypocenterC17C2×#1747
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×C4×C8

930 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103510);