Finite Group DatabasebetaFinite Group Databasebeta| order | 296 |
| isoclinism | isoclinic class of #3866 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #3866 |
| commutator, hypocenter | C37 | C8 |
| Fitting, socle, prime radical | C2×C37 | C4 |
| cosocle | Dic37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 296 |
A minimal faithful permutation representation — 2 generators on 45 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,26)(14,21,19,22)(16,23,24,20)(25,30,31,29)(27,32,33,28)(34,36,37,35)(38,39,40,42,41,43,44,45);(1,2,5,10,19,13,6,11,20,28,31,24,15,22,29,35,37,33,26,17,27,34,36,30,21,8,16,25,32,23,12,3,7,14,18,9,4)Polycyclic presentation:
2^3,37|a^2=b,b^2=c,d^a=d^31,d^b=d^3626 conjugacy classes — view the full character table.
| maximal subgroup of | D37⋊C8, #10596953, C2×#64438, … |
| maximal normal subgroup of | D37⋊C8, #10596953, C2×#64438, … |
| maximal quotient of | #10596927, C2×#64438, C3×#64438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(296, 3);