Finite Group Databasebeta

C22×D461⋊C8 #44443147

order29504
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D461⋊C8
unambiguous semidirect productD461⋊(C22×C8)

Splittings

derived, SylowC461 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#14270406
commutator, hypocenterC461C23×C8
FrattiniC2C23×#14270406
FittingC22×C4×C461C4
socleC23×C461C2×C4
prime radicalC23×D461C4
cosocleDic461C24
LCSG ▷ C461
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1620);