Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×C16 ⋊ C2 |
| Sylow | C7 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | C2×D7 |
| commutator, socle | C2×C7 | C22×C8 |
| Frattini | C8 | C22×D7 |
| Fitting | C2×C7×C16 | C2 |
| prime radical | #1157 | C4 |
| cosocle | C7×C8 | C23 |
| hypercenter | C2×C16 | D7 |
| hypocenter | C7 | #504 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C16 ◁ C2×C16 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,4,6,7,5,3)(8,10,11,18,12,19,21,30,13,20,22,31,23,32,33,38)(9,15,16,27,17,28,29,37,14,24,25,34,26,35,36,39);(9,14)(15,24)(16,25)(17,26)(27,34)(28,35)(29,36)(37,39);(2,3)(4,5)(6,7)(8,9)(10,15)(11,16)(12,17)(13,14)(18,27)(19,28)(20,24)(21,29)(22,25)(23,26)(30,37)(31,34)(32,35)(33,36)(38,39)Polycyclic presentation:
2^6,7|c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^6136 conjugacy classes — view the full character table.
| maximal subgroup of | #11725401, #11725409, #11726810, … |
| maximal normal subgroup of | #11725401, #11725409, #11726810, … |
| maximal quotient of | C16×Dic14, #11726802, #11726805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 435);