Finite Group DatabasebetaFinite Group Databasebeta| order | 18736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C1171 ⋊ M16 |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9368 |
Polycyclic presentation:
2^4,1171|a^2=c,c^2=d,b^a=bd,e^a=e^11704690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49153974, #49153975, #49153976, … |
| maximal normal subgroup of | #49153974, #49153975, #49153976, … |
| maximal quotient of | #49153969, C22⋊(C1171⋊C8), C4⋊(C1171⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18736, 24);