Finite Group DatabasebetaFinite Group Databasebeta| order | 8850 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×#3874 |
| Fitting, socle, Hall | C52×C59 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C59 |
| Hall | C59×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ D3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | #3874 |
| commutator, hypocenter | C52⋊C3 | C2×C59 |
| Frattini | C1 | G |
| Fitting, socle | C52×C59 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C59 | |
24 conjugacy classes of subgroups.
767 conjugacy classes — view the full character table.
| maximal subgroup of | C59×#3874⋊C2, #3874⋊D59, D59×#3874, … |
| maximal normal subgroup of | C59×#3874⋊C2, #3874⋊D59, D59×#3874, … |
| maximal quotient of | C59×#64470, C2×C59×#3874, C59×#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8850, 10);