Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| isoclinism | isoclinic class of Dic94 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic94 |
| Sylow | C47 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D47 |
| commutator, cosocle | C2×C47 | C24 |
| Frattini | C2 | C23×D47 |
| Fitting | C22×C4×C47 | C2 |
| socle, prime radical | C23×C47 | C22 |
| hypercenter | C22×C4 | D47 |
| hypocenter | C47 | C22×Q8 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1504 |
388 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15689027, #15689028, #15689029, … |
| maximal normal subgroup of | #15689027, #15689028, #15689029, … |
| maximal quotient of | C22×Dic47⋊C4, C22×C4⋊Dic47, C2×C4×Dic94, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 186);