Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C139 · Schur multiplier (H2) = C24×C42 |
| direct product | #2309×C139 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C139 | C24 |
| commutator | C22 | C23×C4×C139 |
| Frattini, cosocle | C23 | C24×C139 |
| prime radical | C23×D4×C139 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C139 ◁ G | |
1104 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4448 |
6116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C139×#8748, C139×#8749, C139×#9497, … |
| maximal normal subgroup of | C139×#8748, C139×#8749, C139×#9497, … |
| maximal quotient of | C139×#13775, C139×#13785, C139×#13795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 1041);