Finite Group DatabasebetaFinite Group Databasebeta| order | 368 |
| isoclinism | isoclinic class of Dic46 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C23 ⋊ C2 |
| Sylow | C23 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D23 |
| commutator, socle | C2×C23 | C2×C4 |
| Fitting | C8×C23 | C2 |
| prime radical | C2×D23 | C4 |
| cosocle | C4×C23 | C22 |
| hypercenter | C8 | D23 |
| hypocenter | C23 | M16 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 184 |
A minimal faithful permutation representation — 2 generators on 31 points:
(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,26,29,27,28,30,31);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,28)(29,31)Polycyclic presentation:
2^4,23|b^2=c,c^2=d,b^a=bd,e^a=e^2298 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67262, #10625072, M16×D23, … |
| maximal normal subgroup of | C2×#67262, #10625072, M16×D23, … |
| maximal quotient of | Dic23⋊C8, #10624997, (C2×D23)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(368, 4);