Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C7×#394 ⋊ C2 |
| Sylow | C7 ⋊ #2812 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, cosocle | C23×C7 | C24 |
| Fitting | C7×#394 | C2 |
| hypercenter | #394 | D7 |
| hypocenter | C7 | #2812 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #394 | |
712 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|b^a=be,c^a=cf,h^a=h^6,c^b=cg,d^b=def,h^b=h^6,d^c=de92 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2812, C2×#11734603, #13559962, … |
| maximal normal subgroup of | D7×#2812, C2×#11734603, #13559962, … |
| maximal quotient of | #13284431, #13284432, #13284436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 9369);