Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#1159 |
| Fitting | C7×D4×Q8 ⋊ C2 |
| Sylow | C7 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×D4×Q8 | C2 |
| prime radical | C2×#1159 | C22 |
| hypercenter | D4×Q8 | D7 |
| hypocenter | C7 | Q8×#41 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | #13329773, #13329781, #13329788, … |
| maximal normal subgroup of | #13329773, #13329781, #13329788, … |
| maximal quotient of | C4⋊C4×#1159, Q8×#6440, Q8×#6455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18577);