Finite Group Databasebeta

C2×Dic1123⋊C4 #49090540

order35936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×Dic1123⋊C4

Splittings

SylowC1123 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D1123
commutatorC2×C1123C22×C4
FrattiniC22C22×D1123
FittingC22×C4×C1123C2
socle, prime radicalC23×C1123C22
cosocleC22×C1123C23
hypercenterC22×C4D1123
hypocenterC1123C2×C4⋊C4
LCSG ▷ C2×C1123 ▷ C1123
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35936

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, 100);