Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C79 ⋊ #3502 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | C2×C4×Q8×C79 | C2 |
| prime radical | C23×C79 | C24 |
| hypercenter | C2×C4×Q8 | D79 |
| hypocenter | C79 | #3502 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 | |
964 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 964 conjugacy classes of subgroups — too many to draw. Only its 553 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=g,b^2=f,c^2=g,d^2=f,b^a=bf,c^a=cg,e^a=ef,h^a=h^78,d^b=df1604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34179831, #34179834, #34180268, … |
| maximal normal subgroup of | #34179831, #34179834, #34180268, … |
| maximal quotient of | #34448366, #34448709, #34449207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18320);