Finite Group Databasebeta

D8×Dic461 #44442159

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

Aliases

direct productD8×Dic461

Splittings

SylowC461 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D461
commutatorC4×C461C22×C4
FrattiniC2×C4C22×D461
Fitting, prime radicalC2×D8×C461C2
socleC22×C461C2×D4
cosocleC2×C4×C461C23
hypercenterC2×D8D461
hypocenterC461C4×D8
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

3248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 632);