Finite Group DatabasebetaFinite Group Databasebeta| order | 15536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic971 |
| derived, Sylow | C971 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D971 |
| commutator, hypocenter | C971 | C22×C4 |
| Frattini | C2 | C22×D971 |
| Fitting, socle, prime radical | C23×C971 | C2 |
| cosocle | C2×C971 | C23 |
| LCS | G ▷ C971 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15536 |
3896 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C971⋊#95, C2×C4×Dic971, C2×(C2×D971)⋊C4, … |
| maximal normal subgroup of | C971⋊#95, C2×C4×Dic971, C2×(C2×D971)⋊C4, … |
| maximal quotient of | C2×C4×Dic971, C2×C22⋊Dic971, C2×C4⋊Dic971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15536, 33);