Finite Group DatabasebetaFinite Group Databasebeta| order | 2212 |
| isoclinism | isoclinic class of D79 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D79 |
| unambiguous semidirect product | C79⋊(C22×C7) |
| unambiguous semidirect product | (C2×C79)⋊(C2×C7) |
| Fitting, socle | C2×C7×C79 ⋊ C2 |
| derived, Sylow | C79 ⋊ C22×C7 |
| Hall | C7×C79 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D79 |
| commutator, cosocle, hypocenter | C79 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C79 | C2 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1106 |
574 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D5×D79, C2×C7×D395, C2×C5×C7×D79, … |
| maximal normal subgroup of | C2×C5×C7×D79, C2×C49×D79, C2×C72×D79, … |
| maximal quotient of | C7×D5×D79, C2×C7×D395, C2×C5×C7×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2212, 9);