Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | C82×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1455 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D79 |
| commutator, socle | C22×C79 | C2×C42 |
| Fitting | C82×C79 | C2 |
| prime radical | C22×D79 | C42 |
| cosocle | C42×C79 | C23 |
| hypercenter | C82 | D79 |
| hypocenter | C79 | #1455 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C42 ◁ C82 | |
214 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cf,c^b=cg,h^c=h^782552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34198346, #1455×D79, C2×#23761702, … |
| maximal normal subgroup of | #34198346, #1455×D79, C2×#23761702, … |
| maximal quotient of | #34177644, #34177661, #34178705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2812);