Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C8×Dic83 |
| derived, Sylow | C83 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D83 |
| commutator, hypocenter | C83 | C22×C4×C8 |
| Frattini | C2×C4 | C23×D83 |
| Fitting | C23×C8×C83 | C2 |
| socle, prime radical | C24×C83 | C2×C4 |
| cosocle | C2×C4×C83 | C24 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C23×C8 | |
760 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2752 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×Dic83, #35309555, #35309559, … |
| maximal normal subgroup of | #336×Dic83, #35309555, #35309559, … |
| maximal quotient of | C22×C8×C83⋊C8, C22×#19127423, C2×C8×#13050574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12910);