Finite Group Databasebeta

C22×Dic1844 #44442853

order29504
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1844

Splittings

SylowC461 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1844
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
FittingC22×C8×C461C2
socle, prime radicalC23×C461D4
hypercenterC22×C8D461
hypocenterC461C22×Q16
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

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, 1326);