Finite Group Databasebeta

C2×D4×#6597 #16828165

order3712
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D4×#6597

Splittings

SylowC29 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D29
commutatorC2×C29C23×C8
FrattiniC2×C4C23×D29
FittingC2×C4×D4×C29C2
socleC23×C29C22×C4
prime radicalC22×D4×C29C4
cosocleC2×C4×C29C24
hypercenterC2×C4×D4D29
hypocenterC29C2×C8×D4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 13183);