Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1509 |
242 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=e,c^2=fg,d^2=g,b^a=bd,d^a=df,h^a=h^82,c^b=cf,d^b=dg,e^b=efg1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296283, #35296286, #35296290, … |
| maximal normal subgroup of | #35296283, #35296286, #35296290, … |
| maximal quotient of | #35292398, #35292411, #35292446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 3035);