Finite Group Databasebeta

C22×C4⋊Dic461 #44442527

order29504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊Dic461

Splittings

SylowC461 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D461
commutatorC2×C461C23×C4
FrattiniC22C23×D461
FittingC23×C4×C461C2
socle, prime radicalC24×C461C22
cosocleC22×C461C24
hypercenterC23×C4D461
hypocenterC461C22×C4⋊C4
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

Conjugacy classes & character table

7400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1000);