Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#14579209 |
| Fitting | C23×Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C22×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D79 |
| commutator, cosocle | C2×C79 | C26 |
| Frattini | C2 | C25×D79 |
| Fitting | C23×Q8×C79 | C2 |
| socle | C23×C79 | C24 |
| hypercenter | C23×Q8 | D79 |
| hypocenter | C79 | C22×2−1+4 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
5872 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34287413, #34287440, #34287441, … |
| maximal normal subgroup of | #34287413, #34287440, #34287441, … |
| maximal quotient of | C22×#19099039, C22×#19099041, C22×#19099044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19315);