Finite Group Databasebeta

C2×D4×#63243 #17979691

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×D4×#63243

Splittings

SylowC17 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C4×D4×C17C4
socleC23×C17C23×C4
prime radicalC22×D4×D17C4
cosocleC2×Dic17C25
hypercenterC2×C4×D4#595
hypocenterC17C2×D4×M16
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114935);