Finite Group DatabasebetaFinite Group Databasebeta| order | 884 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#261 |
| Fitting, socle, Hall | C13×C17 ⋊ C4 |
| derived, Sylow | C13 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #261 |
| commutator, hypocenter | C13 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17 | C4 |
| prime radical | C17×D13 | C2 |
| cosocle | D13 | C2×C17 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C17 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 221 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#261, C2×C17×#261, C17×AGL(1,𝔽13), … |
| maximal normal subgroup of | D17×#261, C2×C17×#261, C17×AGL(1,𝔽13), … |
| maximal quotient of | C17×#1057, C2×C17×#261, C3×C17×#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(884, 6);