Finite Group DatabasebetaFinite Group Databasebeta| order | 904 |
| isoclinism | isoclinic class of D113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic113 |
| derived, Sylow | C113 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D113 |
| commutator, hypocenter | C113 | C2×C4 |
| Frattini | C2 | C2×D113 |
| Fitting, socle, prime radical | C22×C113 | C2 |
| cosocle | C2×C113 | C22 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 904 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic113, #14268624, C22⋊Dic113, … |
| maximal normal subgroup of | C4×Dic113, #14268624, C22⋊Dic113, … |
| maximal quotient of | C4×Dic113, C22⋊Dic113, C4⋊Dic113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(904, 7);