Finite Group Databasebeta

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C3×C7×C19⋊#261 #35209129

order20748
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C19⋊#261

Splittings

Fitting, socle, HallC3×C7×C13×C19 ⋊ C4
derived, HallC13×C19 ⋊ C3×C4×C7
HallC7×C13×C19 ⋊ C3×C4
HallC3×C13×C19 ⋊ C4×C7
HallC3×C7×C19 ⋊ #261
HallC3×C7×C13 ⋊ Dic19
HallC7×C19 ⋊ C3×#261
HallC7×C13 ⋊ C3×Dic19
HallC3×C19 ⋊ C7×#261
HallC3×C13 ⋊ C7×Dic19
SylowC19 ⋊ C3×C7×#261
SylowC13 ⋊ C3×C7×Dic19

Subgroups

subgroupG/H
center, hypercenterC3×C7C19⋊#261
commutator, hypocenterC13×C19C3×C4×C7
FrattiniC1G
Fitting, socleC3×C7×C13×C19C4
prime radicalC3×C7×C19×D13C2
cosocleC19×D13C2×C3×C7
LCSG ▷ C13×C19
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5187

Conjugacy classes & character table

1659 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20748, 357);