Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | Aut(G) order 14493696 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2696 |
| Sylow | C337 ⋊ Q32 |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^336,c^b=cd,d^b=de,f^b=f^3362699 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341143, #36341144, #36341145, … |
| maximal normal subgroup of | #36341143, #36341144, #36341145, … |
| maximal quotient of | #36341110, #36341131, C2×Dic2696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 93);