Finite Group DatabasebetaFinite Group Databasebeta| order | 7488 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 84934656 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4 |
| abelian | C22×C32×C42×C13 |
| multiplicative | (ℤ/14469)ˣ, (ℤ/15405)ˣ, (ℤ/16328)ˣ, (ℤ/16432)ˣ, (ℤ/16485)ˣ, (ℤ/16695)ˣ, (ℤ/17584)ˣ, (ℤ/17745)ˣ, (ℤ/18928)ˣ, (ℤ/19292)ˣ, (ℤ/20540)ˣ, (ℤ/21980)ˣ, (ℤ/22608)ˣ, (ℤ/23660)ˣ, (ℤ/24336)ˣ, (ℤ/24492)ˣ, (ℤ/24804)ˣ, (ℤ/28260)ˣ, (ℤ/28938)ˣ, (ℤ/30420)ˣ, (ℤ/30810)ˣ, (ℤ/32970)ˣ, (ℤ/33390)ˣ, (ℤ/35490)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C24×C32×C13 |
| socle, prime radical | C24×C32×C13 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2988 conjugacy classes of subgroups.
7488 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.