Finite Group DatabasebetaFinite Group Databasebeta| order | 11492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C17 ⋊ C4 |
| Sylow | C132 ⋊ #595 |
| Sylow | C17 ⋊ #10621729 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C17 | C4 |
| prime radical, cosocle | C13⋊D221 | C2 |
| LCS | G ▷ C132×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13^2,17|a^2=b,c^a=c^5,d^a=d^8,e^a=e^13,c^b=c^12,d^b=d^12,e^b=e^16722 conjugacy classes — view the full character table.
| maximal subgroup of | #46828210, #46828229, #46828230, … |
| maximal normal subgroup of | #46828229, #46828230, #46828258, … |
| maximal quotient of | C3×#26040109, C3⋊#26040109 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11492, 35);