Finite Group Databasebeta

#106×C19⋊C8 #18073765

order4864
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#106×C19⋊C8

Splittings

SylowC19 ⋊ C8×#106

Subgroups

subgroupG/H
centerC22×C4D4×D19
commutatorC4×C19C2×C4×C8
FrattiniC2×C42C22×D19
FittingC4×C19×#106C2
socle, prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenterC4×#106D19
hypocenterC19C8×#106
LCSG ▷ C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#106

446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4864

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 60794);