Finite Group DatabasebetaFinite Group Databasebeta| order | 17792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C139 · Schur multiplier (H2) = C214 |
| direct product | C22×2−1+4×C139 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C139 | C24 |
| commutator, Frattini, cosocle | C2 | C26×C139 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C139 ◁ G | |
5872 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8896 |
9452 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C139×#20587, C139×#20593, C139×#20603, … |
| maximal normal subgroup of | C139×#20587, C139×#20593, C139×#20603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17792, 2324);