Finite Group Databasebeta

C2×#14529560 #17037845

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14529560

Splittings

SylowC17 ⋊ C2×#1950

Subgroups

subgroupG/H
centerC22×C4C2×D68
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×C4⋊C8C2
socleC23×C17C2×C4⋊C4
prime radicalC24×C17C2×Q8
cosocleC22×C4×C17C24
hypercenterC22×C4⋊C8D17
hypocenterC17C2×#1950
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4⋊C8

938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 173089);