Finite Group Databasebeta

C2×#14526849 #16945875

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14526849

Splittings

SylowC17 ⋊ C2×#1368

Subgroups

subgroupG/H
centerC23#10587479
commutatorC8×C17C22×C8
FrattiniC4×C8C22×D17
FittingC2×C17×#334C2
socle, prime radicalC23×C17#106
cosocleC4×C8×C17C23
hypercenterC2×#334D17
hypocenterC17C2×#1368
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#334

254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 81119);