Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C587 ⋊ C2 |
| Sylow | C587 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D587 |
| commutator, socle | C2×C587 | C22×C4 |
| Fitting | M16×C587 | C2 |
| prime radical | #22627829 | C2 |
| cosocle | C4×C587 | C23 |
| hypercenter | M16 | D587 |
| hypocenter | C587 | #131 |
| LCS | G ▷ C2×C587 ▷ C587 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
Polycyclic presentation:
2^5,587|a^2=d,d^2=e,f^a=f^586,c^b=ce,f^c=f^5862950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49177194, #49177196, #49177199, … |
| maximal normal subgroup of | #49177194, #49177196, #49177199, … |
| maximal quotient of | #49177037, #49177038, #49177045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 154);