Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ #2399 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D83 |
| commutator, socle, prime radical, cosocle | C23×C83 | C24 |
| Frattini | C23 | C23×D83 |
| Fitting | #376×C83 | C2 |
| hypercenter | #376 | D83 |
| hypocenter | C83 | #2399 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
504 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 504 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=e,b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^82,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299477, #35305256, #35305259, … |
| maximal normal subgroup of | #35299477, #35305256, #35305259, … |
| maximal quotient of | #35326148, #35326156, #35326186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7803);