Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C7 ⋊ #2351 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator | C22×C7 | C23×C4 |
| Fitting | C2×C4×C7×Q8 | C2 |
| socle, prime radical, cosocle | C23×C7 | C24 |
| hypercenter | C2×C4×Q8 | D7 |
| hypocenter | C7 | #2351 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
552 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | #13372098, #13372099, #13372117, … |
| maximal normal subgroup of | #13372098, #13372099, #13372117, … |
| maximal quotient of | #13275238, Q8×C7⋊#95, #13275372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14672);