Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#22583606 |
| Fitting | C22×D4×C283 ⋊ C2 |
| Sylow | C283 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D283 |
| commutator, cosocle | C22×C283 | C24 |
| Frattini | C22 | C23×D283 |
| Fitting | C22×D4×C283 | C2 |
| socle | C23×C283 | C23 |
| hypercenter | C22×D4 | D283 |
| hypocenter | C283 | C2×#127 |
| LCS | G ▷ C22×C283 ▷ C283 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
2848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49121656, #49121657, #49121659, … |
| maximal normal subgroup of | #49121656, #49121657, #49121659, … |
| maximal quotient of | C2×#31826334, C2×#31826365, C2×#31826366, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1088);