Finite Group Databasebeta

D8×Dic229 #28411564

order14656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic229

Splittings

SylowC229 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D229
commutatorC4×C229C22×C4
FrattiniC2×C4C22×D229
Fitting, prime radicalC2×D8×C229C2
socleC22×C229C2×D4
cosocleC2×C4×C229C23
hypercenterC2×D8D229
hypocenterC229C4×D8
LCSG ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7328

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 632);