Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of #13063153 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C73 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73 | C22 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28 |
Polycyclic presentation:
2^2,7^3|c^a=c^6,e^a=e^6,c^b=c^6,d^b=d^6103 conjugacy classes — view the full character table.
| derived subgroup of | #72228140 |
| maximal subgroup of | #72228140, #72228141, #72259070, … |
| maximal normal subgroup of | #72228140, #72228141, #72259070, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 34);