Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 73728 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C16×C97 |
| multiplicative | (ℤ/12424)ˣ, (ℤ/18636)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C8 | C23×C97 |
| socle | C23×C97 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
98 conjugacy classes of subgroups.
6208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C97×#1374, C97×#1379, C97×#1380, … |
| maximal normal subgroup of | C97×#1374, C97×#1379, C97×#1380, … |
| maximal quotient of | C2×C4×C16×C97, C2×C22⋊C16×C97, C2×C4⋊C16×C97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 183);