Finite Group Databasebeta

C22×#20300720 #44417227

order29248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#20300720

Splittings

SylowC457 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D457
commutatorC2×C457C23×C4
FrattiniC22C23×D457
FittingC23×C4×C457C2
socle, prime radicalC24×C457C22
cosocleC22×C457C24
hypercenterC23×C4D457
hypocenterC457C22×C4⋊C4
LCSG ▷ C2×C457 ▷ C457
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29248

Conjugacy classes & character table

7336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 999);