Finite Group Databasebeta

C2×D4×#63216 #17978523

order4352
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×#63216

Splittings

SylowC17 ⋊ C2×D4×C16

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C23×C16
FrattiniC2×C4C23×#595
FittingC2×C4×D4×C17C4
socleC23×C17C22×C8
prime radicalC22×D4×C17C8
cosocleC2×#3622C24
hypercenterC2×C4×D4#595
hypocenterC17C2×D4×C16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113767);