Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #2373 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator | C22×C79 | C23×C4 |
| Fitting | #388×C79 | C2 |
| socle, cosocle | C23×C79 | C24 |
| prime radical | C24×C79 | C23 |
| hypercenter | #388 | D79 |
| hypocenter | C79 | #2373 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #388 | |
496 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,h^a=h^78,d^b=de,h^b=h^78,h^c=h^78,h^d=h^781142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2373×D79, C2×#23766527, #34447965, … |
| maximal normal subgroup of | #2373×D79, C2×#23766527, #34447965, … |
| maximal quotient of | #34209725, #34209792, #34209796, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7637);