Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C283 ⋊ #382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D283 |
| commutator | C22×C283 | C22×C4 |
| Fitting | #95×C283 | C2 |
| socle, prime radical, cosocle | C23×C283 | C23 |
| hypercenter | #95 | D283 |
| hypocenter | C283 | #382 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C23 ◁ #95 | |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18112 |
Polycyclic presentation:
2^6,283|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^c=g^2822848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119796, #49119798, #49119819, … |
| maximal normal subgroup of | #49119796, #49119798, #49119819, … |
| maximal quotient of | #49119485, #49119486, Dic283⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 413);