Finite Group Databasebeta

C2×C4×Dic886 #43248182

order28352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic886

Splittings

SylowC443 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D443
commutatorC2×C443C23×C4
FrattiniC22C23×D443
FittingC2×C42×C443C2
socle, prime radicalC23×C443C23
cosocleC22×C443C24
hypercenterC2×C42D443
hypocenterC443C2×C4×Q8
LCSG ▷ C2×C443 ▷ C443
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28352

Conjugacy classes & character table

7112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28352, 1014);