Finite Group Databasebeta

D8×C22⋊Dic83 #35420228

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD8×C22⋊Dic83

Splittings

SylowC83 ⋊ C22⋊C4×D8

Subgroups

subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
Fitting, prime radicalC23×D8×C83C2
socleC23×C83C22×D4
cosocleC22×C4×C83C24
hypercenterC23×D8D83
hypocenterC83C22⋊C4×D8
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

2366 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 185392);