Finite Group Databasebeta

C2×#14526907 #16949285

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14526907

Splittings

SylowC17 ⋊ C2×#1392

Subgroups

subgroupG/H
centerC2×C4#10587505
commutatorC23×C17C2×C42
FrattiniC2×#41C22×D17
FittingC2×C17×#408C2
socleC22×C17#342
prime radicalC22×#41×C17C22
cosocleC2×#41×C17C23
hypercenterC2×#408D17
hypocenterC17C2×#1392
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#408

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84529);