Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D1132 |
| Fitting | C23×C4×C283 ⋊ C2 |
| Sylow | C283 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D283 |
| commutator, cosocle | C2×C283 | C25 |
| Frattini | C2 | C24×D283 |
| Fitting | C23×C4×C283 | C2 |
| socle | C24×C283 | C22 |
| hypercenter | C23×C4 | D283 |
| hypocenter | C283 | C23×D4 |
| LCS | G ▷ C2×C283 ▷ C283 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
4552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119501, #49121181, #49121191, … |
| maximal normal subgroup of | #49119501, #49121181, #49121191, … |
| maximal quotient of | C23×(C2×D283)⋊C4, C23×C4⋊Dic283, C22×C4×D1132, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1371);