Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic47 |
| Sylow | C47 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D47 |
| commutator | C2×C47 | C22×C4 |
| Fitting, prime radical | C2×D4×C47 | C2 |
| socle, cosocle | C22×C47 | C23 |
| hypercenter | C2×D4 | D47 |
| hypocenter | C47 | C4×D4 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #15689203, D8×Dic47, SD16×Dic47, … |
| maximal normal subgroup of | #15689203, D8×Dic47, SD16×Dic47, … |
| maximal quotient of | C22⋊C4×Dic47, C4⋊C4×Dic47, #15688998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 109);