Finite Group Databasebeta

C22×D3736 #44470807

order29888
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC22×D3736

Splittings

FittingC22×C8×C467 ⋊ C2
SylowC467 ⋊ C22×D8

Subgroups

subgroupG/H
centerC23D1868
commutator, cosocleC4×C467C24
FrattiniC4C23×D467
FittingC22×C8×C467C2
socleC23×C467D4
hypercenterC22×C8D467
hypocenterC467C22×D8
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Conjugacy classes & character table

7484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1319);