Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C3⋊D3)⋊A4 |
| commutator, Fitting, cosocle, hypocenter | C32×Q8 | C2×C3 |
| Frattini, socle | C2×C3 | D3×A4 |
| LCS | G ▷ C32×Q8 | |
| UCS | C1 ◁ C2 | |
71 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,5,8)(3,13,12,14,9,7,10,15,4,6,11,16)(18,23,25,20,21,24)(19,22);(1,11,5,9)(2,15,8,13)(3,4,10,12)(6,7,14,16)(17,18,20)(19,21,24)(22,25,23)Polycyclic presentation:
2,3,2^2,3^2,2|a^2=g,c^2=g,d^2=g,e^a=e^2,f^a=f^2,c^b=cd,d^b=c,e^b=ef,d^c=dg26 conjugacy classes — view the full character table.
| maximal subgroup of | #11722254, #11722255, #11722258, … |
| maximal normal subgroup of | #11722254, #11722255, #11722258, … |
| maximal quotient of | #11720765, C2×#88622, #13047037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 269);