Finite Group DatabasebetaFinite Group Databasebeta| order | 816 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C17 ⋊ M16 |
| Sylow | C17 ⋊ ΓL(1,𝔽25) |
| Sylow | C3 ⋊ #63223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D17 |
| commutator, socle | C2×C3×C17 | C2×C4 |
| Fitting, cosocle | C3×C4×C17 | C22 |
| prime radical | C2×D3×C17 | C4 |
| hypocenter | C3×C17 | M16 |
| LCS | G ▷ C2×C3×C17 ▷ C3×C17 | |
| UCS | C1 ◁ C4 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 408 |
Polycyclic presentation:
2^4,3,17|a^2=c,c^2=d,b^a=bd,f^a=f^16,e^b=e^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D17×ΓL(1,𝔽25), #13108983, #13109002, … |
| maximal normal subgroup of | D17×ΓL(1,𝔽25), #13108983, #13109002, … |
| maximal quotient of | #13108694, (C2×D3)⋊#3622, Dic3⋊#3622, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(816, 11);