Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2319 |
540 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 189 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=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35301326, #35301330, #35301340, … |
| maximal normal subgroup of | #35301326, #35301330, #35301340, … |
| maximal quotient of | #35325669, #35325691, #35325708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7148);