Finite Group Databasebeta

C2×C22⋊Dic1123 #49090538

order35936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic1123

Splittings

SylowC1123 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D1123
commutatorC2×C1123C22×C4
FrattiniC22C22×D1123
Fitting, prime radicalC24×C1123C2
socleC23×C1123C22
cosocleC22×C1123C23
hypercenterC24D1123
hypocenterC1123C2×C22⋊C4
LCSG ▷ C2×C1123 ▷ C1123
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17968

Conjugacy classes & character table

8996 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35936, 98);