Finite Group Databasebeta

C2×#28385332 #43272529

order28736
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28385332

Splittings

SylowC449 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D449
commutator, cosocleC22×C449C24
FrattiniC22C23×D449
FittingC2×C42×C449C2
socle, prime radicalC23×C449C23
hypercenterC2×C42D449
hypocenterC449C2×#125
LCSG ▷ C22×C449 ▷ C449
UCSC1 ◁ C23 ◁ C2×C42

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28736

Conjugacy classes & character table

7196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28736, 1071);