Finite Group DatabasebetaFinite Group Databasebeta| order | 792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C11 ⋊ Q8 |
| Sylow | C11 ⋊ #627 |
| Sylow | C32 ⋊ Dic22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C3⋊D3)⋊D11 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C32×C11 | C22 |
| hypocenter | C32×C11 | Q8 |
| LCS | G ▷ C2×C32×C11 ▷ C32×C11 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^3,3^2,11|a^2=c,b^2=c,b^a=bc,d^a=d^2,f^a=f^10,d^b=d^2,e^b=e^275 conjugacy classes — view the full character table.
| maximal subgroup of | #13097230, #13097231, #13097235, … |
| maximal normal subgroup of | #13097230, #13097231, #13097235, … |
| maximal quotient of | #13097109, #13097110, C2×#11716248 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(792, 78);