Finite Group DatabasebetaFinite Group Databasebeta| order | 11388 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C73 ⋊ C3×C4 |
| Hall | C13×#64408 ⋊ C3 |
| Hall | #15667865 ⋊ C4 |
| Hall | #64408 ⋊ C13⋊C3 |
| Sylow | C73 ⋊ C4×C13⋊C3 |
| Sylow | C13 ⋊ #64408⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C73 | C3×C4 |
| prime radical | #19151040 | C2 |
| cosocle | C13×D73 | C2×C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,13,73|a^2=c,e^a=e^27,d^b=d^3,e^b=e^64,e^c=e^72106 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×#64408⋊C3, C3×#26015682, C3⋊#26015682 |
| maximal normal subgroup of | C13⋊C3×#64408⋊C3, C3×#26015682 |
| maximal quotient of | #46802684, C3×#26015682, C3⋊#26015682 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11388, 50);