Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C83 ⋊ #1451 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D83 |
| commutator, socle | C22×C83 | C2×C42 |
| Fitting | #431×C83 | C2 |
| prime radical | C23×C83 | C42 |
| cosocle | C42×C83 | C23 |
| hypercenter | #431 | D83 |
| hypocenter | C83 | #1451 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C42 ◁ #431 | |
208 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 121 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=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^a=h^82,h^b=h^821696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35294971, #35294975, #35294976, … |
| maximal normal subgroup of | #35294971, #35294975, #35294976, … |
| maximal quotient of | #35293767, #35293787, #35294831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2800);