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.
| Sylow | C23 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D23 |
| commutator, socle | C2×C23 | C2×C4 |
| Fitting | C2×C4×C23 | C2 |
| prime radical | C22×C23 | C4 |
| cosocle | C4×C23 | C22 |
| hypercenter | C2×C4 | D23 |
| hypocenter | C23 | M16 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
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)(25,28)(29,31);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25,26,29,27,28,30,31)Polycyclic presentation:
2^4,23|a^2=c,c^2=d,b^a=bd,e^a=e^2298 conjugacy classes — view the full character table.
| maximal subgroup of | #10624987, #10625001, #10625004, … |
| maximal normal subgroup of | #10624987, #10625001, #10625004, … |
| maximal quotient of | #10624985, C4⋊(C23⋊C8), C22⋊(C23⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(368, 9);