Finite Group DatabasebetaFinite Group Databasebeta| order | 9100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D35×D65 |
| Fitting, socle, derived, Hall | C52×C7×C13 ⋊ C22 |
| Hall | C52×C13 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ D52 |
| Sylow | C52 ⋊ D7×D13 |
| Sylow | C13 ⋊ D5×D35 |
| Sylow | C7 ⋊ D5×D65 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C13 | C22 |
| LCS | G ▷ C52×C7×C13 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
646 conjugacy classes — view the full character table.
| maximal subgroup of | #41031578, #41031697, #41031698, … |
| maximal normal subgroup of | #41031697, #41031698, D65×C5⋊AGL(1,𝔽7), … |
| maximal quotient of | C3×D35×D65, D65×D105, D35×D195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9100, 103);