Finite Group DatabasebetaFinite Group Databasebeta| order | 296 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C37 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D37 |
| commutator, hypocenter | C37 | C8 |
| Fitting, cosocle | C4×C37 | C2 |
| socle, prime radical | C2×C37 | C4 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C4 | |
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)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39,40,42,41,43,44,45);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)Polycyclic presentation:
2^3,37|a^2=b,b^2=c,d^a=d^3680 conjugacy classes — view the full character table.
| maximal subgroup of | #10596927, C8×D37, #10596929, … |
| maximal normal subgroup of | #10596927, C8×D37, #10596929, … |
| maximal quotient of | #10596925, C2×#64436, C3×#64436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(296, 1);