Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×D7×Q16 |
| Fitting | C4×C7×Q16 ⋊ C2 |
| Sylow | C7 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#1332, #13263547, D7×#1334, … |
| maximal normal subgroup of | D7×#1332, #13263547, D7×#1334, … |
| maximal quotient of | C8×D7×Q16, D7×#1584, D7×#1591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11927);