Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #117×C283 ⋊ C2 |
| Sylow | C283 ⋊ #556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D283 |
| commutator, socle, cosocle | C22×C283 | C24 |
| Fitting | #117×C283 | C2 |
| prime radical | C2×C22⋊D283 | C22 |
| hypercenter | #117 | D283 |
| hypocenter | C283 | #556 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ #117 | |
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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=ef,c^2=e,d^2=e,b^a=be,c^a=cf,d^b=de,g^c=g^2822845 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49133174, #49133176, #49133196, … |
| maximal normal subgroup of | #49133174, #49133176, #49133196, … |
| maximal quotient of | #49124150, #49124154, #49124211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1267);