Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | #394×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2500 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #394×C79 | C2 |
| prime radical | C2×#14579133 | C2 |
| hypercenter | #394 | D79 |
| hypocenter | C79 | #2500 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #394 | |
568 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=eg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^d=h^78896 conjugacy classes — view the full character table.
| maximal subgroup of | #2500×D79, C2×#23767857, #34457898, … |
| maximal normal subgroup of | #2500×D79, C2×#23767857, #34457898, … |
| maximal quotient of | #34210240, #34210800, #34211442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8967);