Finite Group DatabasebetaFinite Group Databasebeta| order | 18081 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#89204 |
| derived, Sylow | C72 ⋊ C9×C41 |
| Hall | C72×C41 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | #3861 |
| commutator, hypocenter | C72 | C9×C41 |
| Frattini | C3 | C41×#3861 |
| Fitting, socle, prime radical | C3×C72×C41 | C3 |
| cosocle | C3×C72 | C3×C41 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3×C41 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18081 |
2337 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#11725077, C41⋊#11725077, C41×#11725076, … |
| maximal normal subgroup of | C41×#11725077, C41⋊#11725077, C41×#11725076, … |
| maximal quotient of | C2×C41×#89204 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18081, 7);