Finite Group Databasebeta

D8×Dic389 #38734182

order24896
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic389

Splittings

SylowC389 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D389
commutatorC4×C389C22×C4
FrattiniC2×C4C22×D389
Fitting, prime radicalC2×D8×C389C2
socleC22×C389C2×D4
cosocleC2×C4×C389C23
hypercenterC2×D8D389
hypocenterC389C4×D8
LCSG ▷ C4×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

2744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 632);