Finite Group DatabasebetaFinite Group Databasebeta| order | 828 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×#157 |
| Fitting, socle, Hall | C32×C23 ⋊ C4 |
| derived, Sylow | C32 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #157 |
| commutator, hypocenter | C32 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23 | C4 |
| prime radical | C3⋊D3×C23 | C2 |
| cosocle | C3⋊D3 | C2×C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 138 |
138 conjugacy classes — view the full character table.
| maximal subgroup of | C23×AGL(1,𝔽9), C23⋊AGL(1,𝔽9), #157×D23, … |
| maximal normal subgroup of | C23×AGL(1,𝔽9), C23⋊AGL(1,𝔽9), #157×D23, … |
| maximal quotient of | C23×#622, C2×C23×#157, C5×C23×#157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(828, 17);