Finite Group DatabasebetaFinite Group Databasebeta| order | 9824 |
| automorphism | Aut(G) order 12024576 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2456 |
| Sylow | C307 ⋊ Q32 |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,307|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^306,c^b=cd,d^b=de,f^b=f^3062459 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34087725, #34087726, #34087727, … |
| maximal normal subgroup of | #34087725, #34087726, #34087727, … |
| maximal quotient of | #34087692, #34087713, C2×Dic2456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9824, 93);