Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#17985391 |
| Fitting | C22×D4×C283 ⋊ C2 |
| Sylow | C283 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D283 |
| commutator, cosocle | C2×C283 | C25 |
| Frattini | C2 | C24×D283 |
| Fitting | C22×D4×C283 | C2 |
| socle | C23×C283 | C23 |
| hypercenter | C22×D4 | D283 |
| hypocenter | C283 | C22×#41 |
| LCS | G ▷ C2×C283 ▷ C283 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
2860 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49121177, #49121186, #49121198, … |
| maximal normal subgroup of | #49121177, #49121186, #49121198, … |
| maximal quotient of | C22×#22583566, C22×#22583568, C22×(C22⋊D283)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1375);