Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C137 · Schur multiplier (H2) = C28 |
| direct product | C22×#95×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C25×C137 | C22 |
| commutator | C2 | C22×C42×C137 |
| Frattini, cosocle | C23 | C24×C137 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C25×C137 ◁ G | |
1880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
10960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#7554, C137×#7555, C137×#7556, … |
| maximal normal subgroup of | C137×#7554, C137×#7555, C137×#7556, … |
| maximal quotient of | C2×C4×#95×C137, C2×C22⋊#95×C137, C2×C4⋊#95×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 998);