Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C17 ⋊ #41 |
| Sylow | C17 ⋊ #237 |
| Sylow | C3 ⋊ #63252 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D17 |
| commutator, socle, cosocle | C2×C3×C17 | C23 |
| Fitting | C22×C3×C17 | C22 |
| hypercenter | C22 | D3×D17 |
| hypocenter | C3×C17 | #41 |
| LCS | G ▷ C2×C3×C17 ▷ C3×C17 | |
| UCS | C1 ◁ C2 ◁ C22 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 408 |
Polycyclic presentation:
2^4,3,17|b^2=d,c^a=cd,f^a=f^16,e^b=e^2111 conjugacy classes — view the full character table.
| maximal subgroup of | #13109741, D3×#63252, #13109761, … |
| maximal normal subgroup of | #13109741, D3×#63252, #13109761, … |
| maximal quotient of | #13109021, #13109023, #13109024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 136);