Finite Group Databasebeta

D8×Dic443 #43247800

order28352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic443

Splittings

SylowC443 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D443
commutatorC4×C443C22×C4
FrattiniC2×C4C22×D443
Fitting, prime radicalC2×D8×C443C2
socleC22×C443C2×D4
cosocleC2×C4×C443C23
hypercenterC2×D8D443
hypocenterC443C4×D8
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14176

Conjugacy classes & character table

3122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28352, 632);