Finite Group DatabasebetaFinite Group Databasebeta| order | 11492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C17 ⋊ C4 |
| Sylow | C132 ⋊ Dic17 |
| Sylow | C17 ⋊ #10621728 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C17 | C4 |
| prime radical, cosocle | C17×C13⋊D13 | C2 |
| LCS | G ▷ C132×C17 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13^2,17|a^2=b,c^a=c^5,d^a=d^5,e^a=e^16,c^b=c^12,d^b=d^12734 conjugacy classes — view the full character table.
| maximal subgroup of | #46828235, #46828256, #46828292, … |
| maximal normal subgroup of | #46828235, #46828256, #46828292, … |
| maximal quotient of | C3×#26040107, C3⋊#26040107 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11492, 33);