Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C139 · Schur multiplier (H2) = C25 |
| direct product | #1442×C139 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C139 | C23 |
| commutator | C23 | C22×C4×C139 |
| Frattini, cosocle | C24 | C23×C139 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C139 ◁ G | |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17792 |
6116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C139×#7122, C139×#8867, C139×#8869, … |
| maximal normal subgroup of | C139×#7122, C139×#8867, C139×#8869, … |
| maximal quotient of | C139×#7556, C139×#7557, C139×#11255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 174);