Finite Group Databasebeta

C2×#14527081 #16999944

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8

Aliases

direct productC2×#14527081

Splittings

SylowC17 ⋊ C2×#1453

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC22×C17C22×C42
FrattiniC42C23×D17
FittingC2×C4×M16×C17C2
socleC23×C17C2×C42
prime radicalC24×C17C42
cosocleC42×C17C24
hypercenterC2×C4×M16D17
hypocenterC17C2×#1453
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135188);