Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#19127609 |
| Fitting | C23×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D83 |
| commutator, cosocle | C23×C83 | C24 |
| Frattini | C23 | C23×D83 |
| Fitting | C23×D4×C83 | C2 |
| socle | C24×C83 | C23 |
| hypercenter | C23×D4 | D83 |
| hypocenter | C83 | C2×#392 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299410, #35299425, #35304597, … |
| maximal normal subgroup of | #35299410, #35299425, #35304597, … |
| maximal quotient of | C2×#24905702, C2×#24905704, C2×#24905705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7705);