Finite Group Databasebeta

C2×#28385397 #43272976

order28736
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28385397

Splittings

SylowC449 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#14267798
commutatorC2×C449C22×C8
FrattiniC22C22×#14267798
FittingC22×C4×C449C4
socleC23×C449C2×C4
prime radicalC23×D449C4
cosocleC2×Dic449C23
hypercenterC22×C4#14267798
hypocenterC449C2×C22⋊C8
LCSG ▷ C2×C449 ▷ C449
UCSC1 ◁ C23 ◁ C22×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14368

Conjugacy classes & character table

1832 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28736, 1518);