Finite Group Databasebeta

C22×Dic1828 #44417554

order29248
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic1828

Splittings

SylowC457 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D1828
commutator, cosocleC4×C457C24
FrattiniC4C23×D457
FittingC22×C8×C457C2
socle, prime radicalC23×C457D4
hypercenterC22×C8D457
hypocenterC457C22×Q16
LCSG ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29248

Conjugacy classes & character table

7324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 1326);