Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #384×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2354 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator | C22×C79 | C23×C4 |
| Fitting | #384×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| prime radical | C22×D316 | C22 |
| hypercenter | #384 | D79 |
| hypocenter | C79 | #2354 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #384 | |
632 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^78,d^b=de,h^b=h^781142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34182447, #34182451, #34182475, … |
| maximal normal subgroup of | #34182447, #34182451, #34182475, … |
| maximal quotient of | #34209693, #34209709, #34209750, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7461);