Finite Group DatabasebetaFinite Group Databasebeta| order | 6076 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C7⋊D7)⋊D31 |
| unambiguous semidirect product | D217⋊D7 |
| Fitting, socle, derived, Hall | C72×C31 ⋊ C22 |
| Sylow | C72 ⋊ C2×D31 |
| Sylow | C31 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C31 | C22 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7^2,31|c^a=c^6,e^a=e^30,c^b=c^6,d^b=d^6415 conjugacy classes — view the full character table.
| maximal subgroup of | #32912146, #32912147, #64424⋊D31, … |
| maximal normal subgroup of | #32912146, #32912147, #64424⋊D31, … |
| maximal quotient of | C3×(C7⋊D7)⋊D31, D217⋊D21, #32912279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6076, 21);