Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #123×C283 ⋊ C2 |
| Sylow | C283 ⋊ #536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D283 |
| commutator, socle, cosocle | C22×C283 | C24 |
| Fitting | #123×C283 | C2 |
| prime radical | C2×#17985391 | C2 |
| hypercenter | #123 | D283 |
| hypocenter | C283 | #536 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #123 | |
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9056 |
Polycyclic presentation:
2^6,283|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^2821996 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49122913, #49130665, #536×D283, … |
| maximal normal subgroup of | #49122913, #49130665, #536×D283, … |
| maximal quotient of | #49123846, #49123848, #49123880, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1121);