Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #2980 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D79 |
| commutator, socle | C22×C79 | C23×C4 |
| Fitting, prime radical | #532×C79 | C2 |
| cosocle | C2×C4×C79 | C24 |
| hypercenter | #532 | D79 |
| hypocenter | C79 | #2980 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
394 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 197 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,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^78,c^b=ce,d^b=dg,d^c=dg1130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34182671, #34182674, #34183216, … |
| maximal normal subgroup of | #34182671, #34182674, #34183216, … |
| maximal quotient of | #34286996, #34287033, #34287252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13581);