Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C19 ⋊ C4×C9 |
| Hall | #14555740 ⋊ C4 |
| Hall | C19×#261 ⋊ C9 |
| Hall | #261 ⋊ #4296 |
| Sylow | C19 ⋊ #261⋊C9 |
| Sylow | C13 ⋊ C4×#4296 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C19 | C4×C9 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,13,19|a^2=c,b^3=d,e^a=e^5,e^b=e^3,f^b=f^16,e^c=e^12,f^d=f^1153 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×#4296, #72277847 |
| maximal normal subgroup of | AGL(1,𝔽13)×#4296, #72277847 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 141);