Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| isoclinism | isoclinic class of D175 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C2×C17×D175 |
| unambiguous semidirect product | (C2×C7)⋊(C17×D25) |
| unambiguous semidirect product | (C2×C25)⋊(D7×C17) |
| Fitting | C2×C7×C17×C25 ⋊ C2 |
| derived, Hall | C7×C25 ⋊ C22×C17 |
| Hall | C7×C17×C25 ⋊ C22 |
| Hall | C17×C25 ⋊ C2×D7 |
| Hall | C7×C17 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D7×C17 |
| Sylow | C7 ⋊ C2×C17×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D175 |
| commutator, cosocle, hypocenter | C7×C25 | C22×C17 |
| Frattini | C5 | C2×C17×D35 |
| Fitting | C2×C7×C17×C25 | C2 |
| socle | C2×C5×C7×C17 | D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C2×C17 | |
60 conjugacy classes of subgroups.
3026 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×ΓL(1,𝔽8)⋊D25, D3×C17×D175, C2×C17×D525, … |
| maximal normal subgroup of | C2×C17×ΓL(1,𝔽8)⋊D25, C2×C3×C17×D175 |
| maximal quotient of | D3×C17×D175, C2×C17×D525, C2×C3×C17×D175 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 30);