Finite Group DatabasebetaFinite Group Databasebeta| order | 18416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D4604 |
| Fitting | C2×C4×C1151 ⋊ C2 |
| Sylow | C1151 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D1151 |
| commutator, cosocle | C2×C1151 | C23 |
| Frattini | C2 | C22×D1151 |
| Fitting | C2×C4×C1151 | C2 |
| socle | C22×C1151 | C22 |
| hypercenter | C2×C4 | D1151 |
| hypocenter | C1151 | C2×D4 |
| LCS | G ▷ C2×C1151 ▷ C1151 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9208 |
4610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49145761, #49145765, #49145767, … |
| maximal normal subgroup of | #49145761, #49145765, #49145767, … |
| maximal quotient of | C2×(C2×D1151)⋊C4, C2×C4⋊Dic1151, C4×D4604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18416, 36);