Finite Group Databasebeta

C2×C22⋊Dic1087 #46852140

order34784
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic1087

Splittings

SylowC1087 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D1087
commutatorC2×C1087C22×C4
FrattiniC22C22×D1087
Fitting, prime radicalC24×C1087C2
socleC23×C1087C22
cosocleC22×C1087C23
hypercenterC24D1087
hypocenterC1087C2×C22⋊C4
LCSG ▷ C2×C1087 ▷ C1087
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17392

Conjugacy classes & character table

8708 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34784, 98);