Finite Group DatabasebetaFinite Group Databasebeta| order | 18784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#22627828 |
| Fitting | C2×D4×C587 ⋊ C2 |
| Sylow | C587 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D587 |
| commutator, cosocle | C2×C587 | C24 |
| Frattini | C2 | C23×D587 |
| Fitting | C2×D4×C587 | C2 |
| socle | C22×C587 | C23 |
| hypercenter | C2×D4 | D587 |
| hypocenter | C587 | C2×#41 |
| LCS | G ▷ C2×C587 ▷ C587 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9392 |
2950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49177052, #49177061, #49177073, … |
| maximal normal subgroup of | #49177052, #49177061, #49177073, … |
| maximal quotient of | C2×#34037577, C2×#34037579, C2×(C22⋊D587)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18784, 188);