Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×C7⋊#95 |
| Sylow | C7 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D7 |
| commutator | C2×C7 | C43 |
| Frattini | C24 | C22×D7 |
| Fitting | C22×C42×C7 | C2 |
| socle, prime radical, cosocle | C24×C7 | C23 |
| hypercenter | C22×C42 | D7 |
| hypocenter | C7 | C4×#95 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 | |
752 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13240327, #13240354, #13240356, … |
| maximal normal subgroup of | #13240327, #13240354, #13240356, … |
| maximal quotient of | #13241715, #13241716, C4×#89345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 4053);