Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #2780 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#386 | C2 |
| prime radical | C22×C7×D4 | C22 |
| hypercenter | #386 | D7 |
| hypocenter | C7 | #2780 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #386 | |
464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=ef,d^2=eg,b^a=bef,c^a=cfg,d^a=deg,h^a=h^6,c^b=cg,d^b=def,h^b=h^6116 conjugacy classes — view the full character table.
| maximal subgroup of | #13561385, #13561387, #13561398, … |
| maximal normal subgroup of | #13561385, #13561387, #13561398, … |
| maximal quotient of | #13281589, #13281798, #13282192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 7068);