Finite Group DatabasebetaFinite Group Databasebeta| order | 9488 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14558631 |
| Fitting | C4×C593 ⋊ C4 |
| Sylow | C593 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14558631 |
| commutator, socle | C2×C593 | C2×C4 |
| Fitting | C4×C593 | C4 |
| prime radical, cosocle | C2×D593 | C22 |
| hypercenter | C4 | #14558631 |
| hypocenter | C593 | C4⋊C4 |
| LCS | G ▷ C2×C593 ▷ C593 | |
| UCS | C1 ◁ C2 ◁ C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,593|a^2=d,b^2=c,b^a=bc,e^a=e^77,e^d=e^592602 conjugacy classes — view the full character table.
| maximal subgroup of | #34039347, #34039348, #34039353, … |
| maximal normal subgroup of | #34039347, #34039348, #34039353, … |
| maximal quotient of | (C2×#14558631)⋊C4, C4⋊#18011661, #34039352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9488, 46);