Finite Group Databasebeta

D19×#1302 #18072793

order4864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productD19×#1302

Splittings

FittingC19×#1302 ⋊ C2
SylowC19 ⋊ C2×#1302

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#1302C2
socleC22×C19C2×#95
prime radicalC23×D19C4⋊C4
cosocleC2×C42×C19C23
hypercenter#1302D19
hypocenterC19C2×#1302
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 59822);