Finite Group DatabasebetaFinite Group Databasebeta| order | 304 |
| isoclinism | isoclinic class of Dic38 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D19 |
| commutator, socle, cosocle | C2×C19 | C23 |
| Frattini | C2 | C22×D19 |
| Fitting | C2×C4×C19 | C2 |
| hypercenter | C2×C4 | D19 |
| hypocenter | C19 | #41 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 152 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(21,25)(24,27);(20,22,23,26)(21,24,25,27);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,24)(23,25)(26,27)Polycyclic presentation:
2^4,19|b^2=d,c^a=cd,e^a=e^1882 conjugacy classes — view the full character table.
| maximal subgroup of | #10597262, #10597282, #10597347, … |
| maximal normal subgroup of | #10597262, #10597282, #10597347, … |
| maximal quotient of | C4×Dic38, #10597316, #10597318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(304, 30);