Finite Group DatabasebetaFinite Group Databasebeta| order | 9212 |
| automorphism | Aut(G) order 8898792 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2303 |
| unambiguous semidirect product | C47⋊Dic49 |
| unambiguous semidirect product | C49⋊Dic47 |
| derived, Hall | C47×C49 ⋊ C4 |
| Sylow | C49 ⋊ Dic47 |
| Sylow | C47 ⋊ Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2303 |
| commutator, hypocenter | C47×C49 | C4 |
| Frattini | C2×C7 | D329 |
| Fitting | C2×C47×C49 | C2 |
| socle | C2×C7×C47 | D7 |
| LCS | G ▷ C47×C49 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,47,2,7|a^2=d,b^7=e^6,b^a=b^6e,c^a=c^46,e^a=e^62306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47⋊((C49⋊C3)⋊C4), C3×Dic2303, Dic6909, … |
| maximal normal subgroup of | C47⋊((C49⋊C3)⋊C4), C3×Dic2303, Dic4606 |
| maximal quotient of | C3×Dic2303, Dic6909, Dic16121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9212, 4);