Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C7×#126 ⋊ C2 |
| Sylow | C7 ⋊ #2480 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C2×C7×#126 | C2 |
| prime radical | C24×D7 | C22 |
| hypercenter | C2×#126 | D7 |
| hypocenter | C7 | #2480 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^2=ef,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^6122 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2480, C2×#11740526, #13521563, … |
| maximal normal subgroup of | D7×#2480, C2×#11740526, #13521563, … |
| maximal quotient of | #13275711, #13276002, #13276609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15292);