Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #392×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2617 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | #392×C83 | C2 |
| hypercenter | #392 | D83 |
| hypocenter | C83 | #2617 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ #392 | |
824 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 143 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=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^d=h^82934 conjugacy classes — view the full character table.
| maximal subgroup of | #35314582, #35315071, #35378235, … |
| maximal normal subgroup of | #35314582, #35315071, #35378235, … |
| maximal quotient of | #35330757, #35330791, #35330917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 10243);