Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C7×#392 ⋊ C2 |
| Sylow | C7 ⋊ #14715 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator, socle, cosocle | C24×C7 | C24 |
| Fitting | C2×C7×#392 | C2 |
| hypercenter | C2×#392 | D7 |
| hypocenter | C7 | #14715 |
| LCS | G ▷ C24×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#392 | |
7490 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^8,7|b^a=be,c^a=cf,d^a=dh,c^b=cg,i^d=i^6196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 100941);