Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #2523 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #393×C83 | C2 |
| prime radical | C24×C83 | C23 |
| hypercenter | #393 | D83 |
| hypocenter | C83 | #2523 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #393 | |
420 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 129 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=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=cg,h^c=h^82,h^d=h^82940 conjugacy classes — view the full character table.
| maximal subgroup of | #35316685, #35316689, #35317271, … |
| maximal normal subgroup of | #35316685, #35316689, #35317271, … |
| maximal quotient of | #35326510, #35327756, #35328288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9243);