Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #534×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14581761 |
| commutator, cosocle | C24×C83 | C23 |
| Frattini | C24 | C22×D83 |
| Fitting | #534×C83 | C2 |
| socle | C22×C83 | #120 |
| hypercenter | #534 | D83 |
| hypocenter | C83 | #2021 |
| LCS | G ▷ C24×C83 ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #534 | |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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=bd,c^a=ce,f^a=fg,c^b=cf,h^b=h^82,d^c=dg928 conjugacy classes — view the full character table.
| maximal subgroup of | #35316431, #35316436, #35316448, … |
| maximal normal subgroup of | #35316431, #35316436, #35316448, … |
| maximal quotient of | #35304598, #35304605, #35304612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 5634);