Finite Group Databasebeta

C2×#14527223 #17000752

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14527223

Splittings

SylowC17 ⋊ C2×#1489

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC42C23×D17
FittingC2×C4×#41×C17C2
socleC23×C17C2×C22⋊C4
prime radicalC22×#41×C17C4
cosocleC42×C17C24
hypercenterC2×C4×#41D17
hypocenterC17C2×#1489
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

1378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135996);