Finite Group DatabasebetaFinite Group Databasebeta| order | 1452 |
| isoclinism | isoclinic class of #10624391 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C112⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #10624391 |
| commutator, hypocenter | C112⋊C3 | C4 |
| Fitting, socle | C2×C112 | D3 |
| prime radical, cosocle | C2×C112⋊C3 | C2 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 132 |
Polycyclic presentation:
2^2,3,11^2|a^2=b,c^a=c^2,d^a=d^6e^6,e^a=d^7e^5,d^c=d^6e^6,e^c=d^2e^476 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13089712, C3⋊#13089712, C13×#13089712, … |
| maximal normal subgroup of | C3×#13089712, C13×#13089712, C17×#13089712, … |
| maximal quotient of | #17983705, C3×#13089712, C3⋊#13089712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1452, 11);