Finite Group Databasebeta

C2×#14526860 #16945917

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

Aliases

direct productC2×#14526860

Splittings

SylowC17 ⋊ C2×#1373

Subgroups

subgroupG/H
centerC2×C8D136
commutatorC8×C17C22×C8
FrattiniC4×C8C22×D17
FittingC2×C4×C16×C17C2
socleC22×C17#335
prime radicalC23×C17#108
cosocleC4×C8×C17C23
hypercenterC2×C4×C16D17
hypocenterC17C2×#1373
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C4×C16

230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

1112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 81161);