Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×C7⋊C32 |
| derived, Sylow | C7 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D7 |
| commutator, hypocenter | C7 | C4×C32 |
| Frattini | C2×C16 | C2×D7 |
| Fitting | C4×C7×C16 | C2 |
| socle, prime radical | C22×C7 | C2×C16 |
| cosocle | C2×C7×C16 | C22 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C7⋊C8, C8×C7⋊C32, #13241123, … |
| maximal normal subgroup of | C32×C7⋊C8, C8×C7⋊C32, #13241123, … |
| maximal quotient of | C8×C7⋊C32, #13241127, #13241483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 79);