Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#88324 |
| derived, Sylow | C53 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #6157 |
| commutator, hypocenter | C53 | C22×C8 |
| Frattini | C2 | C22×#6157 |
| Fitting, socle, prime radical | C23×C53 | C4 |
| cosocle | Dic53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #16811489, C2×C4×#88324, C2×#13133272, … |
| maximal normal subgroup of | #16811489, C2×C4×#88324, C2×#13133272, … |
| maximal quotient of | C2×C4×#88324, C2×C22⋊#88324, C2×C4⋊#88324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 228);