Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C181 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D181 |
| commutator | C22×C181 | C22×C4 |
| Fitting, prime radical | C25×C181 | C2 |
| socle, cosocle | C23×C181 | C23 |
| hypercenter | C25 | D181 |
| hypocenter | C181 | #379 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=f,b^a=bd,c^a=ce,g^a=g^1802908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37531625, #37533635, #37533636, … |
| maximal normal subgroup of | #37531625, #37533635, #37533636, … |
| maximal quotient of | #37531944, #37531962, #37531992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 405);