Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q82×D79 |
| Fitting | Q82×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | Q82×C79 | C2 |
| prime radical | C22×D79 | C24 |
| hypercenter | Q82 | D79 |
| hypocenter | C79 | C2×Q82 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1112 conjugacy classes of subgroups; only the 575 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 575 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1025 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1623×D79, #1633×D79, #1645×D79, … |
| maximal normal subgroup of | #1623×D79, #1633×D79, #1645×D79, … |
| maximal quotient of | Q8×C4⋊C4×D79, #2369×D79, Q8×#14579126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18084);