Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D283 |
| Fitting | C32×C283 ⋊ C2 |
| derived, Sylow | C283 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D283 |
| commutator, hypocenter | C283 | C2×C32 |
| Frattini | C16 | C2×D283 |
| Fitting | C32×C283 | C2 |
| socle | C2×C283 | C2×C16 |
| prime radical | C2×D283 | C16 |
| cosocle | C16×C283 | C22 |
| LCS | G ▷ C283 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
4576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D283, #49119471, C2×C32×D283, … |
| maximal normal subgroup of | C64×D283, #49119471, C2×C32×D283, … |
| maximal quotient of | C32×Dic283, (C2×D283)⋊C32, Dic283⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 380);