Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#90335 |
| Fitting | C2×C7×C22⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#538 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D7 |
| commutator, cosocle | C22×C7 | C25 |
| Frattini | C22 | C24×D7 |
| Fitting | C2×C7×C22⋊Q8 | C2 |
| socle | C23×C7 | C24 |
| hypercenter | C2×C22⋊Q8 | D7 |
| hypocenter | C7 | C2×#538 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
1336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #13245625, #13245629, C2×#11728731, … |
| maximal normal subgroup of | #13245625, #13245629, C2×#11728731, … |
| maximal quotient of | C2×#11731449, C2×#11731828, C2×#11732037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17811);