Finite Group DatabasebetaFinite Group Databasebeta| order | 12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#87604 |
| Fitting, socle, derived, Hall | C31×C97 ⋊ C4 |
| Sylow | C97 ⋊ Dic31 |
| Sylow | C31 ⋊ #87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C97 | C4 |
| prime radical, cosocle | C31×D97 | C2 |
| LCS | G ▷ C31×C97 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,31,97|a^2=b,c^a=c^30,d^a=d^75,d^b=d^96778 conjugacy classes — view the full character table.
| maximal subgroup of | #49115329, #49115330, (C31⋊C3)⋊#87604, … |
| maximal normal subgroup of | #49115329, #49115330, (C31⋊C3)⋊#87604, … |
| maximal quotient of | C3×C31⋊#87604, C3⋊(C31⋊#87604) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12028, 7);