Finite Group Databasebeta

C2×#14529376 #17036476

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14529376

Splittings

SylowC17 ⋊ C2×#1921

Subgroups

subgroupG/H
centerC24C2×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C4×C4⋊C4×C17C2
socle, prime radicalC24×C17C2×D4
cosocleC22×C4×C17C24
hypercenterC2×C4×C4⋊C4D17
hypocenterC17C2×#1921
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171720);