Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #568×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3585 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D316 |
| commutator, cosocle | C4×C79 | C25 |
| Frattini | C4 | C24×D79 |
| Fitting | #568×C79 | C2 |
| socle | C2×C79 | C23×D4 |
| hypercenter | #568 | D79 |
| hypocenter | C79 | #3585 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|f^2=g,b^a=bf,e^a=eg,f^a=fg,h^a=h^78,f^b=fg,h^b=h^78,d^c=dg1367 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34319565, #34319566, #34319587, … |
| maximal normal subgroup of | #34319565, #34319566, #34319587, … |
| maximal quotient of | #35151841, #35151854, #35151954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19291);