Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD64×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2262 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D79 |
| commutator, cosocle | C16×C79 | C23 |
| Frattini | C16 | C22×D79 |
| Fitting | SD64×C79 | C2 |
| socle | C2×C79 | C2×D16 |
| hypercenter | SD64 | D79 |
| hypocenter | C79 | #2262 |
| LCS | G ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
106 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^78,h^c=h^78779 conjugacy classes — view the full character table.
| maximal subgroup of | #2262×D79, C2×#23765708, #34446411, … |
| maximal normal subgroup of | #2262×D79, C2×#23765708, #34446411, … |
| maximal quotient of | #34208700, #34208702, #34208771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6818);