Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2984 |
364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,h^b=h^82,h^d=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35375590, #35375592, #35375598, … |
| maximal normal subgroup of | #35375590, #35375592, #35375598, … |
| maximal quotient of | #35403145, #35403466, #35403474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13598);