Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic194 |
| Sylow | C97 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D97 |
| commutator | C2×C97 | C22×C4 |
| Frattini | C22 | C22×D97 |
| Fitting | C42×C97 | C2 |
| socle, prime radical, cosocle | C22×C97 | C23 |
| hypercenter | C42 | D97 |
| hypocenter | C97 | C4×Q8 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3104 |
788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 112);