Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #2667 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #381×C79 | C2 |
| prime radical | C24×C79 | C23 |
| hypercenter | #381 | D79 |
| hypocenter | C79 | #2667 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #381 | |
408 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=g,c^2=eg,d^2=f,b^a=be,c^a=cf,c^b=cg,h^b=h^78,d^c=de1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34191485, #34191486, #34191492, … |
| maximal normal subgroup of | #34191485, #34191486, #34191492, … |
| maximal quotient of | #34214891, #34214904, #34214990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10706);