Finite Group DatabasebetaFinite Group Databasebeta| order | 9100 |
| isoclinism | isoclinic class of #63122 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×#63122 |
| Fitting, socle, Hall | C52×C7×C13 ⋊ C4 |
| derived | C5×C13 ⋊ C4×C5×C7 |
| Hall | C52×C13 ⋊ C4×C7 |
| Hall | C52×C7 ⋊ #261 |
| Hall | C7×C13 ⋊ C5×AGL(1,𝔽5) |
| Sylow | C52 ⋊ C7×#261 |
| Sylow | C13 ⋊ C5×C7×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | #63122 |
| commutator, hypocenter | C5×C13 | C4×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C13 | C4 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C5×C7 | |
52 conjugacy classes of subgroups.
700 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7×#63122⋊C3, C5×#19129737, C5×#19129739, … |
| maximal normal subgroup of | C5×C7×#63122⋊C3, C5×#19129737, C5×#19129739, … |
| maximal quotient of | C3×C5×C7×#63122, C5×C7×C3⋊#63122 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9100, 53);