Finite Group Databasebeta

C22×#20301491 #44442852

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

Aliases

direct productC22×#20301491

Splittings

SylowC461 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23C22⋊D461
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
FittingC22×Q8×C461C2
socle, prime radicalC23×C461D4
hypercenterC22×Q8D461
hypocenterC461C22×Q16
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

Conjugacy classes & character table

4628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1325);