Finite Group DatabasebetaFinite Group Databasebeta| order | 388 |
| isoclinism | isoclinic class of #87604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C97 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C97 | C4 |
| prime radical, cosocle | D97 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 97 |
A minimal faithful permutation representation — 2 generators on 97 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,86)(53,72,73,82)(57,76,77,80)(61,79,74,78)(65,81,70,75)(67,83,84,71)(85,90,91,89)(87,92,93,88)(94,96,97,95);(1,2,5,10,19,32,49,70,64,45,62,80,72,47,67,85,92,83,63,42,25,12,3,7,14,23,36,53,74,60,43,28,41,58,78,68,87,94,96,90,81,59,38,21,8,16,27,40,57,77,56,39,26,15,24,37,54,75,89,95,97,93,86,79,55,34,17,29,44,61,73,52,35,22,13,6,11,20,33,50,71,88,91,84,66,82,76,51,30,46,65,69,48,31,18,9,4)Polycyclic presentation:
2^2,97|a^2=b,c^a=c^22,c^b=c^9628 conjugacy classes — view the full character table.
| maximal subgroup of | #11715906, C2×#87604, #87604⋊C3, … |
| maximal normal subgroup of | #11715906, C2×#87604, #87604⋊C3, … |
| maximal quotient of | #11715897, C2×#87604, C3×#87604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(388, 3);