Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#22583658 |
| Fitting | C22×Q8×C283 ⋊ C2 |
| Sylow | C283 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D283 |
| commutator, cosocle | C2×C283 | C25 |
| Frattini | C2 | C24×D283 |
| Fitting | C22×Q8×C283 | C2 |
| socle | C22×C283 | C24 |
| hypercenter | C22×Q8 | D283 |
| hypocenter | C283 | C2×2−1+4 |
| LCS | G ▷ C2×C283 ▷ C283 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
2854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49121219, #49121222, #49121233, … |
| maximal normal subgroup of | #49121219, #49121222, #49121233, … |
| maximal quotient of | C2×#31826941, C2×#31826943, C2×#31826946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1383);