Finite Group DatabasebetaFinite Group Databasebeta| order | 904 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D113 |
| Fitting | C22×C113 ⋊ C2 |
| Sylow | C113 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D113 |
| commutator, socle, cosocle | C2×C113 | C22 |
| Fitting | C22×C113 | C2 |
| hypercenter | C22 | D113 |
| hypocenter | C113 | D4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 452 |
Polycyclic presentation:
2^3,113|b^a=bc,d^a=d^112229 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D113, C2×C22⋊D113, #14268646, … |
| maximal normal subgroup of | D4×D113, C2×C22⋊D113, #14268646, … |
| maximal quotient of | #14268624, C22⋊Dic113, #14268626, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(904, 8);