Finite Group Databasebeta

C2×#28385261 #43271994

order28736
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#28385261

Splittings

SylowC449 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D449
commutatorC4×C449C22×C4
FrattiniC2×C4C22×D449
Fitting, prime radicalC22×D4×C449C2
socleC23×C449D4
cosocleC2×C4×C449C23
hypercenterC22×D4D449
hypocenterC449C2×#102
LCSG ▷ C4×C449 ▷ C2×C449 ▷ C449
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14368

Conjugacy classes & character table

4508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28736, 536);