Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C587 ⋊ C2 |
| Sylow | C587 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D587 |
| commutator, socle, cosocle | C22×C587 | C23 |
| Fitting | C4⋊C4×C587 | C2 |
| prime radical | C22×D587 | C22 |
| hypercenter | C4⋊C4 | D587 |
| hypocenter | C587 | #126 |
| LCS | G ▷ C22×C587 ▷ C587 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
Polycyclic presentation:
2^5,587|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^586,f^c=f^5862944 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D587, C2×#34037616, #49177607, … |
| maximal normal subgroup of | #126×D587, C2×#34037616, #49177607, … |
| maximal quotient of | #49176947, #49176961, #49176963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 141);