Finite Group DatabasebetaFinite Group Databasebeta| order | 9100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D175 |
| unambiguous semidirect product | (C7×D13)⋊D25 |
| unambiguous semidirect product | (C25×D13)⋊D7 |
| Fitting, derived, Hall | C7×C13×C25 ⋊ C22 |
| Hall | C13×C25 ⋊ C2×D7 |
| Hall | C7×C25 ⋊ C2×D13 |
| Hall | C7×C13 ⋊ C2×D25 |
| Sylow | C25 ⋊ D7×D13 |
| Sylow | C13 ⋊ C2×D175 |
| Sylow | C7 ⋊ D13×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C7×C13×C25 | C22 |
| Frattini | C5 | D13×D35 |
| socle | C5×C7×C13 | C2×D5 |
| LCS | G ▷ C7×C13×C25 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
712 conjugacy classes — view the full character table.
| maximal subgroup of | #10587716⋊D25, #10587717⋊D25, D13×ΓL(1,𝔽8)⋊D25, … |
| maximal normal subgroup of | #10587716⋊D25, #10587717⋊D25, D13×ΓL(1,𝔽8)⋊D25, … |
| maximal quotient of | C3×D13×D175, D13×D525, D39×D175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9100, 24);