Finite Group Databasebeta

C22×D3688 #44442846

order29504
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC22×D3688

Splittings

FittingC22×C8×C461 ⋊ C2
SylowC461 ⋊ C22×D8

Subgroups

subgroupG/H
centerC23D1844
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
FittingC22×C8×C461C2
socleC23×C461D4
hypercenterC22×C8D461
hypocenterC461C22×D8
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

7388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1319);