Finite Group Databasebeta

C2×#14545354 #17979422

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14545354

Splittings

FittingC2×C17×#131 ⋊ C4
SylowC17 ⋊ C2×#2875

Subgroups

subgroupG/H
centerC2×C4C23×#595
commutatorC2×C17C23×C42
FrattiniC4C24×#595
FittingC2×C17×#131C4
socleC22×C17C22×C42
prime radicalC2×#41×D17C22
cosocleC4×D17C25
hypercenterC2×#131#595
hypocenterC17C2×#2875
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×#131

3278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114666);