Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | B(4,𝔽2)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3026 |
800 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|b^a=be,c^a=cf,d^a=dg,f^b=fg,e^c=eg,h^d=h^82685 conjugacy classes — view the full character table.
| maximal subgroup of | #35558458, #35558460, #35558469, … |
| maximal normal subgroup of | #35558458, #35558460, #35558469, … |
| maximal quotient of | #35378235, #35378242, #35378249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13905);