Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D4×D19 |
| Fitting | C3×D4×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ C2×D4 |
| Sylow | C19 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×D19 |
| commutator, cosocle | C2×C19 | C23×C3 |
| Frattini | C2 | C22×C3×D19 |
| Fitting | C3×D4×C19 | C2 |
| socle | C2×C3×C19 | C23 |
| hypercenter | C3×D4 | D19 |
| hypocenter | C19 | C2×C3×D4 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2×C3 ◁ C3×D4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 228 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#213, D19×#214, #14269406, … |
| maximal normal subgroup of | D19×#213, D19×#214, #14269406, … |
| maximal quotient of | C3×#10597324, C3×#10597331, C3×C22⋊C4×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 177);