Finite Group Databasebeta

C22×D3704 #44445563

order29632
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC22×D3704

Splittings

FittingC22×C8×C463 ⋊ C2
SylowC463 ⋊ C22×D8

Subgroups

subgroupG/H
centerC23D1852
commutator, cosocleC4×C463C24
FrattiniC4C23×D463
FittingC22×C8×C463C2
socleC23×C463D4
hypercenterC22×C8D463
hypocenterC463C22×D8
LCSG ▷ C4×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14816

Conjugacy classes & character table

7420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 1319);