Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #397×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #397×C83 | C2 |
| prime radical | C2×#14581765 | C2 |
| hypercenter | #397 | D83 |
| hypocenter | C83 | #2504 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #397 | |
596 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 141 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,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^d=h^82940 conjugacy classes — view the full character table.
| maximal subgroup of | #35378015, #35378018, #35378033, … |
| maximal normal subgroup of | #35378015, #35378018, #35378033, … |
| maximal quotient of | #35326391, #35326801, #35327586, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 8997);