Finite Group Databasebeta

C2×#14527163 #17000673

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14527163

Splittings

FittingC2×C17×D4⋊C8 ⋊ C2
SylowC17 ⋊ C2×#1476

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC2×C17×D4⋊C8C2
socleC23×C17C2×C22⋊C4
prime radicalC22×#63254C4
cosocleC42×C17C24
hypercenterC2×D4⋊C8D17
hypocenterC17C2×#1476
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

1430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135917);