Finite Group Databasebeta

#487×Dic79 #34296246

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4

Aliases

direct product#487×Dic79

Splittings

SylowC79 ⋊ C4×#487

Subgroups

subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#487×C79C2
socle, prime radicalC23×C79C22×D4
cosocleC22×C4×C79C24
hypercenterC2×#487D79
hypocenterC79C4×#487
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20224

Conjugacy classes & character table

1804 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 177545);