Finite Group Databasebeta

C2×D4×#6127 #16769879

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×D4×#6127

Splittings

FittingC22×C4×D4×C13 ⋊ C2
SylowC13 ⋊ C2×D4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C4×D4×C13C2
socleC23×C13C25
hypercenterC22×C4×D4D13
hypocenterC13C2×D4×#41
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

12314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076528);