Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2369 |
496 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 261 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=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^82,d^b=de,h^b=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298861, #35298865, #35298868, … |
| maximal normal subgroup of | #35298861, #35298865, #35298868, … |
| maximal quotient of | #35325844, #35325954, #35326020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7600);