Finite Group Databasebeta

← Prev (#49144704) Next (#49144706) →

C7×C19×Dic69 #49144705

order36708
automorphism?
homologyAbelianization (H1) = C4×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19×Dic69
unambiguous semidirect productC3⋊(C7×C19×Dic23)
unambiguous semidirect productC23⋊(C7×Dic3×C19)

Splittings

derived, HallC3×C23 ⋊ C4×C7×C19
HallC3×C7×C19×C23 ⋊ C4
HallC7×C19×C23 ⋊ Dic3
HallC3×C19×C23 ⋊ C4×C7
HallC3×C7×C23 ⋊ C4×C19
HallC19×C23 ⋊ C7×Dic3
HallC3×C7×C19 ⋊ Dic23
HallC7×C23 ⋊ Dic3×C19
HallC3×C19 ⋊ C7×Dic23
SylowC23 ⋊ C7×Dic3×C19
HallC3×C7 ⋊ C19×Dic23
SylowC3 ⋊ C7×C19×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C19D69
commutator, hypocenterC3×C23C4×C7×C19
FrattiniC2C7×C19×D69
Fitting, socle, prime radicalC2×C3×C7×C19×C23C2
cosocleC2×C3×C23C2×C7×C19
LCSG ▷ C3×C23
UCSC1 ◁ C2×C7×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36708

Conjugacy classes & character table

9576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36708, 14);