Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C137 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊C4×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C137 | C24 |
| commutator | C22 | C23×C4×C137 |
| Frattini, cosocle | C23 | C24×C137 |
| prime radical | C23×D4×C137 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C137 ◁ G | |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
6850 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#9255, C137×#9259, D4×#99×C137, … |
| maximal normal subgroup of | C137×#9255, C137×#9259, D4×#99×C137, … |
| maximal quotient of | C22⋊C42×C137, C22⋊C4×C4⋊C4×C137, D4×#95×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 1070);