Finite Group Databasebeta

D8×#14270406 #44443112

order29504
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×#14270406

Splittings

FittingD8×C461 ⋊ C4
SylowC461 ⋊ C4×D8

Subgroups

subgroupG/H
centerC2D4×#14270406
commutatorC4×C461C22×C4
FrattiniC4C22×#14270406
FittingD8×C461C4
socleC2×C461C4×D4
prime radicalD8×D461C2
cosocleC4×D461C23
hypercenterD8#14270406
hypocenterC461C4×D8
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2 ◁ C4 ◁ D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3688

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 1585);