Finite Group DatabasebetaFinite Group Databasebeta| order | 18976 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C593 ⋊ C2 |
| Sylow | C593 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D593 |
| commutator, socle, cosocle | C22×C593 | C23 |
| Fitting | C4⋊C4×C593 | C2 |
| prime radical | C22×D593 | C22 |
| hypercenter | C4⋊C4 | D593 |
| hypocenter | C593 | #126 |
| LCS | G ▷ C22×C593 ▷ C593 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9488 |
Polycyclic presentation:
2^5,593|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^592,f^c=f^5922974 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D593, C2×#34039280, #49183242, … |
| maximal normal subgroup of | #126×D593, C2×#34039280, #49183242, … |
| maximal quotient of | #49182582, #49182596, #49182598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18976, 141);