Finite Group DatabasebetaFinite Group Databasebeta| order | 304 |
| isoclinism | isoclinic class of Dic38 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D19 |
| commutator, socle | C2×C19 | C2×C4 |
| Fitting | C2×C4×C19 | C2 |
| prime radical | C22×C19 | C4 |
| cosocle | C4×C19 | C22 |
| hypercenter | C2×C4 | D19 |
| hypocenter | C19 | M16 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 152 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(21,24)(25,27);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21,22,25,23,24,26,27)Polycyclic presentation:
2^4,19|a^2=c,c^2=d,b^a=bd,e^a=e^1882 conjugacy classes — view the full character table.
| maximal subgroup of | #10597262, #10597276, #10597279, … |
| maximal normal subgroup of | #10597262, #10597276, #10597279, … |
| maximal quotient of | #10597260, C4⋊(C19⋊C8), C22⋊(C19⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(304, 9);