Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C587 ⋊ C2 |
| Sylow | C587 ⋊ #135 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
Polycyclic presentation:
2^5,587|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^586,d^b=de,f^b=f^5864702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49176886, #49176888, #49176889, … |
| maximal normal subgroup of | #49176886, #49176888, #49176889, … |
| maximal quotient of | #49177077, #49177118, C4×D4696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 168);