Finite Group Databasebeta

C2×#14544586 #17968571

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14544586

Splittings

FittingC2×C4×C8×C17 ⋊ C4
SylowC17 ⋊ C2×#1772

Subgroups

subgroupG/H
centerC2×C8C4⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC22×C17C4×C4⋊C4
prime radicalC23×D17#41
cosocleC2×C4×D17C24
hypercenterC2×C4×C8#595
hypocenterC17C2×#1772
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

1102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103815);