Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C7⋊C32 |
| derived, Sylow | C7 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D7 |
| commutator, hypocenter | C7 | C22×C32 |
| Frattini | C16 | C22×D7 |
| Fitting | C22×C7×C16 | C2 |
| socle, prime radical | C23×C7 | C16 |
| cosocle | C7×C16 | C23 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13241482, #13241483, #13241494, … |
| maximal normal subgroup of | #13241482, #13241483, #13241494, … |
| maximal quotient of | C2×C4×C7⋊C32, C2×C22⋊(C7⋊C32), C2×C4⋊(C7⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 3915);