Finite Group Databasebeta

C2×#14526852 #16945886

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14526852

Splittings

SylowC17 ⋊ C2×#1369

Subgroups

subgroupG/H
centerC2×C4#10587488
commutatorC8×C17C22×C8
FrattiniC4×C8C22×D17
FittingC2×C17×#346C2
socleC22×C17#334
prime radicalC23×C17#108
cosocleC4×C8×C17C23
hypercenterC2×#346D17
hypocenterC17C2×#1369
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×#346

222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 81130);