Finite Group DatabasebetaFinite Group Databasebeta| order | 2124 |
| isoclinism | isoclinic class of C3⋊D177 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D177 |
| unambiguous semidirect product | (C2×C3)⋊D177 |
| unambiguous semidirect product | (C2×C59)⋊(C3⋊D3) |
| Fitting, socle | C2×C32×C59 ⋊ C2 |
| derived, Hall | C32×C59 ⋊ C22 |
| Sylow | C59 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D177 |
| commutator, cosocle, hypocenter | C32×C59 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C59 | C2 |
| LCS | G ▷ C32×C59 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1062 |
534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C3⋊D177, C2×C3⋊D1239, C2×C7×C3⋊D177, … |
| maximal normal subgroup of | C2×C7×C3⋊D177, C2×C11×C3⋊D177, C2×C13×C3⋊D177, … |
| maximal quotient of | D7×C3⋊D177, C2×C3⋊D1239, C2×C7×C3⋊D177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2124, 26);