Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10625350 |
| Fitting | C22×C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D47 |
| commutator, cosocle | C2×C47 | C24 |
| Frattini | C2 | C23×D47 |
| Fitting | C22×C4×C47 | C2 |
| socle | C22×C47 | C23 |
| hypercenter | C22×C4 | D47 |
| hypocenter | C47 | C2×#41 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15689088, #15689089, #15689091, … |
| maximal normal subgroup of | #15689088, #15689089, #15689091, … |
| maximal quotient of | C2×#13093981, C2×#13093983, C2×C4×C22⋊D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 189);