Finite Group Databasebeta

C2×#14526827 #16945544

order4352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14526827

Splittings

SylowC17 ⋊ C2×#1360

Subgroups

subgroupG/H
centerC23#10587503
commutatorC2×C8×C17C22×C4
FrattiniC4×C8C22×D17
FittingC2×C17×#495C2
socleC23×C17#102
prime radicalC22×D8×C17C4
cosocleC4×C8×C17C23
hypercenterC2×#495D17
hypocenterC17C2×#1360
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#495

434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 80788);