Finite Group DatabasebetaFinite Group Databasebeta| order | 5008 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6289920 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C24×C313 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
134 conjugacy classes of subgroups.
5008 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C22⋊C4×C313, #120×C313, C22×D4×C313, … |
| maximal normal subgroup of | C2×C22⋊C4×C313, #120×C313, C22×D4×C313, … |
| maximal quotient of | C22×D4×C313, C22×Q8×C313, C2×#41×C313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5008, 14);