Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #1917 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D79 |
| commutator, socle, prime radical | C23×C79 | C22×C4 |
| Fitting | #336×C79 | C2 |
| cosocle | C22×C4×C79 | C23 |
| hypercenter | #336 | D79 |
| hypocenter | C79 | #1917 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cg,h^b=h^78,h^c=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1917×D79, C2×#23763963, #34290331, … |
| maximal normal subgroup of | #1917×D79, C2×#23763963, #34290331, … |
| maximal quotient of | #34186413, #34186420, #34186427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5073);