Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M64×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C22×D79 |
| commutator, socle | C2×C79 | C22×C16 |
| Fitting | M64×C79 | C2 |
| prime radical | #11929624 | C8 |
| cosocle | C16×C79 | C23 |
| hypercenter | M64 | D79 |
| hypocenter | C79 | #2258 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C16 ◁ M64 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^78,c^b=cg,h^c=h^781640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34208830, #34208832, #34208835, … |
| maximal normal subgroup of | #34208830, #34208832, #34208835, … |
| maximal quotient of | #34208450, #34208451, #34208464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6805);