Finite Group Databasebeta

#332×Dic83 #35295354

order21248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#332×Dic83

Splittings

SylowC83 ⋊ C4×#332

Subgroups

subgroupG/H
centerC23C22⋊C4×D83
commutatorC2×C4×C83C2×C42
FrattiniC2×C42C22×D83
FittingC2×#332×C83C2
socle, prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenterC2×#332D83
hypocenterC83C4×#332
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21248

Conjugacy classes & character table

1634 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 60518);