Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C283 ⋊ C2 |
| Sylow | C283 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D283 |
| commutator, socle | C2×C283 | C22×C8 |
| Fitting | M32×C283 | C2 |
| prime radical | #17985392 | C4 |
| cosocle | C8×C283 | C23 |
| hypercenter | M32 | D283 |
| hypocenter | C283 | #504 |
| LCS | G ▷ C2×C283 ▷ C283 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|a^2=d,d^2=e,e^2=f,g^a=g^282,c^b=cf,g^c=g^2822860 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49123095, #49123097, #49123100, … |
| maximal normal subgroup of | #49123095, #49123097, #49123100, … |
| maximal quotient of | #49122859, #49122860, #49122873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 967);