Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C139 · Schur multiplier (H2) = C26 |
| direct product | C2×#397×C139 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C139 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C139 |
| prime radical | C25×C139 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C139 ◁ G | |
820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8896 |
6116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C139×#9025, C139×#9028, C139×#9918, … |
| maximal normal subgroup of | C139×#9025, C139×#9028, C139×#9918, … |
| maximal quotient of | C2×#1439×C139, C2×#1440×C139, C2×#1442×C139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 1122);